Arc Schemes And Singularities

Arc Schemes And Singularities

Author: David Bourqui

Publisher: World Scientific

Published: 2020-03-05

Total Pages: 312

ISBN-13: 1786347210

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This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.


Book Synopsis Arc Schemes And Singularities by : David Bourqui

Download or read book Arc Schemes And Singularities written by David Bourqui and published by World Scientific. This book was released on 2020-03-05 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.

Handbook of Geometry and Topology of Singularities IV

Handbook of Geometry and Topology of Singularities IV

Author: José Luis Cisneros-Molina

Publisher: Springer Nature

Published: 2023-11-10

Total Pages: 622

ISBN-13: 3031319257

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This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.


Book Synopsis Handbook of Geometry and Topology of Singularities IV by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities IV written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2023-11-10 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Algebraic Geometry: Salt Lake City 2015 (Part 1)

Algebraic Geometry: Salt Lake City 2015 (Part 1)

Author: Tommaso de Fernex

Publisher: American Mathematical Soc.

Published: 2018-06-01

Total Pages: 655

ISBN-13: 1470435772

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This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.


Book Synopsis Algebraic Geometry: Salt Lake City 2015 (Part 1) by : Tommaso de Fernex

Download or read book Algebraic Geometry: Salt Lake City 2015 (Part 1) written by Tommaso de Fernex and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

The Geometry of Schemes

The Geometry of Schemes

Author: David Eisenbud

Publisher: Springer Science & Business Media

Published: 2006-04-06

Total Pages: 265

ISBN-13: 0387226397

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Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.


Book Synopsis The Geometry of Schemes by : David Eisenbud

Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Combinatorics and Physics

Combinatorics and Physics

Author: Kurusch Ebrahimi-Fard

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 480

ISBN-13: 0821853295

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This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.


Book Synopsis Combinatorics and Physics by : Kurusch Ebrahimi-Fard

Download or read book Combinatorics and Physics written by Kurusch Ebrahimi-Fard and published by American Mathematical Soc.. This book was released on 2011 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.

Jet Schemes and Truncated Wedge Schemes

Jet Schemes and Truncated Wedge Schemes

Author: Cornelia Oichi Yuen

Publisher:

Published: 2006

Total Pages: 208

ISBN-13:

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Book Synopsis Jet Schemes and Truncated Wedge Schemes by : Cornelia Oichi Yuen

Download or read book Jet Schemes and Truncated Wedge Schemes written by Cornelia Oichi Yuen and published by . This book was released on 2006 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Representations and Nilpotent Orbits of Lie Algebraic Systems

Representations and Nilpotent Orbits of Lie Algebraic Systems

Author: Maria Gorelik

Publisher: Springer Nature

Published: 2019-10-18

Total Pages: 553

ISBN-13: 3030235319

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This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.


Book Synopsis Representations and Nilpotent Orbits of Lie Algebraic Systems by : Maria Gorelik

Download or read book Representations and Nilpotent Orbits of Lie Algebraic Systems written by Maria Gorelik and published by Springer Nature. This book was released on 2019-10-18 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Algebra, Geometry and Their Interactions

Algebra, Geometry and Their Interactions

Author: Alberto Corso

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 282

ISBN-13: 0821840940

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This volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.


Book Synopsis Algebra, Geometry and Their Interactions by : Alberto Corso

Download or read book Algebra, Geometry and Their Interactions written by Alberto Corso and published by American Mathematical Soc.. This book was released on 2007 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.

Algebraic Geometry

Algebraic Geometry

Author: Dan Abramovich

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 539

ISBN-13: 0821847031

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Offers information on various technical tools, from jet schemes and derived categories to algebraic stacks. This book delves into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. It describes various advances in higher-dimensional bi rational geometry.


Book Synopsis Algebraic Geometry by : Dan Abramovich

Download or read book Algebraic Geometry written by Dan Abramovich and published by American Mathematical Soc.. This book was released on 2009 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers information on various technical tools, from jet schemes and derived categories to algebraic stacks. This book delves into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. It describes various advances in higher-dimensional bi rational geometry.

$p$-Adic Analysis, Arithmetic and Singularities

$p$-Adic Analysis, Arithmetic and Singularities

Author: Carlos Galindo

Publisher: American Mathematical Society

Published: 2022-05-11

Total Pages: 311

ISBN-13: 1470467798

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This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications. This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces $p$-adic analysis, the theory of Archimedean, $p$-adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists. This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.


Book Synopsis $p$-Adic Analysis, Arithmetic and Singularities by : Carlos Galindo

Download or read book $p$-Adic Analysis, Arithmetic and Singularities written by Carlos Galindo and published by American Mathematical Society. This book was released on 2022-05-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications. This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces $p$-adic analysis, the theory of Archimedean, $p$-adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists. This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.