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Birational Geometry and Moduli Spaces

Author: Elisabetta Colombo

Publisher: Springer Nature

Published: 2020-02-25

Total Pages: 200

ISBN-13: 303037114X

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This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.

Book Synopsis Birational Geometry and Moduli Spaces by : Elisabetta Colombo

Download or read book Birational Geometry and Moduli Spaces written by Elisabetta Colombo and published by Springer Nature. This book was released on 2020-02-25 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.

Algebraic Geometry and Number Theory

Author: Hussein Mourtada

Publisher: Birkhäuser

Published: 2017-05-16

Total Pages: 232

ISBN-13: 9783319477787

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This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Book Synopsis Algebraic Geometry and Number Theory by : Hussein Mourtada

Download or read book Algebraic Geometry and Number Theory written by Hussein Mourtada and published by Birkhäuser. This book was released on 2017-05-16 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Geometry of Moduli

Author: Jan Arthur Christophersen

Publisher: Springer

Published: 2018-11-24

Total Pages: 326

ISBN-13: 3319948814

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The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

Book Synopsis Geometry of Moduli by : Jan Arthur Christophersen

Download or read book Geometry of Moduli written by Jan Arthur Christophersen and published by Springer. This book was released on 2018-11-24 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

The Geometry of Moduli Spaces of Sheaves

Author: Daniel Huybrechts

Publisher: Cambridge University Press

Published: 2010-05-27

Total Pages: 345

ISBN-13: 1139485822

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This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts

Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Birational Geometry of Moduli Spaces of Pointed Curves

Author: Irene Schwarz

Publisher:

Published: 2020

Total Pages:

ISBN-13:

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Book Synopsis Birational Geometry of Moduli Spaces of Pointed Curves by : Irene Schwarz

Download or read book Birational Geometry of Moduli Spaces of Pointed Curves written by Irene Schwarz and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Birational Geometry of the Moduli Spaces of Curves with One Marked Point

Author: David Hay Jensen

Publisher:

Published: 2010

Total Pages: 144

ISBN-13:

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Book Synopsis Birational Geometry of the Moduli Spaces of Curves with One Marked Point by : David Hay Jensen

Download or read book Birational Geometry of the Moduli Spaces of Curves with One Marked Point written by David Hay Jensen and published by . This book was released on 2010 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Birational Geometry of Moduli Spaces of Stable Objects on Enriques Surfaces

Author: Thorsten Beckmann

Publisher:

Published: 2018

Total Pages:

ISBN-13:

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Book Synopsis Birational Geometry of Moduli Spaces of Stable Objects on Enriques Surfaces by : Thorsten Beckmann

Download or read book Birational Geometry of Moduli Spaces of Stable Objects on Enriques Surfaces written by Thorsten Beckmann and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Birational Geometry, Rational Curves, and Arithmetic

Author: Fedor Bogomolov

Publisher: Springer Science & Business Media

Published: 2013-05-17

Total Pages: 324

ISBN-13: 146146482X

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This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Book Synopsis Birational Geometry, Rational Curves, and Arithmetic by : Fedor Bogomolov

Download or read book Birational Geometry, Rational Curves, and Arithmetic written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2013-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Birational Geometry of Hypersurfaces

Author: Andreas Hochenegger

Publisher: Springer Nature

Published: 2019-10-08

Total Pages: 297

ISBN-13: 3030186385

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Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.

Book Synopsis Birational Geometry of Hypersurfaces by : Andreas Hochenegger

Download or read book Birational Geometry of Hypersurfaces written by Andreas Hochenegger and published by Springer Nature. This book was released on 2019-10-08 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.

The Birational Geometry of [moduli Space M(3)] and [moduli Space M(2,1)]

Author: William Frederick Rulla

Publisher:

Published: 2001

Total Pages: 376

ISBN-13:

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"The cones of effective, nef and moving divisors are determined for the moduli spaces [M with macron-subscript 3] and [M with macron-subscript 2,1]. Every nef Cartier divisor in both spaces is shown to be semi-ample in characteristic zero. A decomposition of the cone of effective divisors [NE with macron-superscript 1] ([M with macron-subscript 3]) into chambers parametrizing [sic] contracting birational maps is given and is shown to pull back to an analogous decomposion [sic] of [NE with macron-superscript 1] ([M with macron-subscript 2,1]). In particular, a divisor on [M with macron-subscript 3] is nef (resp. moving) if and only if its pull-back to [M with macron-subscript 2,1] is. Every birational morphism of [M with macron-subscript 2,1] to a normal projective variety is induced from [M with macron-subscript 3], and has an analagous [sic] exceptional locus."--Page vi.

Book Synopsis The Birational Geometry of [moduli Space M(3)] and [moduli Space M(2,1)] by : William Frederick Rulla

Download or read book The Birational Geometry of [moduli Space M(3)] and [moduli Space M(2,1)] written by William Frederick Rulla and published by . This book was released on 2001 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The cones of effective, nef and moving divisors are determined for the moduli spaces [M with macron-subscript 3] and [M with macron-subscript 2,1]. Every nef Cartier divisor in both spaces is shown to be semi-ample in characteristic zero. A decomposition of the cone of effective divisors [NE with macron-superscript 1] ([M with macron-subscript 3]) into chambers parametrizing [sic] contracting birational maps is given and is shown to pull back to an analogous decomposion [sic] of [NE with macron-superscript 1] ([M with macron-subscript 2,1]). In particular, a divisor on [M with macron-subscript 3] is nef (resp. moving) if and only if its pull-back to [M with macron-subscript 2,1] is. Every birational morphism of [M with macron-subscript 2,1] to a normal projective variety is induced from [M with macron-subscript 3], and has an analagous [sic] exceptional locus."--Page vi.