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These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
Book Synopsis Lectures on Curves on an Algebraic Surface by : David Mumford
Download or read book Lectures on Curves on an Algebraic Surface written by David Mumford and published by Princeton University Press. This book was released on 1966-08-21 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
Book Synopsis Lectures on Curves on an Algebraic Surface by : David Mumford
Download or read book Lectures on Curves on an Algebraic Surface written by David Mumford and published by . This book was released on 1985 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Curves on an Algebraic Surface by : Frederick Charles Barghoorn
Download or read book Lectures on Curves on an Algebraic Surface written by Frederick Charles Barghoorn and published by . This book was released on 1966 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Book Synopsis Singularities of Plane Curves by : Eduardo Casas-Alvero
Download or read book Singularities of Plane Curves written by Eduardo Casas-Alvero and published by Cambridge University Press. This book was released on 2000-08-31 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas. "This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson
Book Synopsis Introduction to the Theory of Schemes by : Yuri I. Manin
Download or read book Introduction to the Theory of Schemes written by Yuri I. Manin and published by Springer. This book was released on 2018-05-15 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas. "This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson
We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5a
Book Synopsis Geometric Invariant Theory for Polarized Curves by : Gilberto Bini
Download or read book Geometric Invariant Theory for Polarized Curves written by Gilberto Bini and published by Springer. This book was released on 2014-11-07 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5a
Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Book Synopsis Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 by : Robion C. Kirby
Download or read book Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 written by Robion C. Kirby and published by Princeton University Press. This book was released on 2016-03-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Book Synopsis Algebraic Geometry, Arcata 1974 by : Robin Hartshorne
Download or read book Algebraic Geometry, Arcata 1974 written by Robin Hartshorne and published by American Mathematical Soc.. This book was released on 1975-12-31 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt:
The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.
Book Synopsis Geometry of Algebraic Curves by : Enrico Arbarello
Download or read book Geometry of Algebraic Curves written by Enrico Arbarello and published by Springer Science & Business Media. This book was released on 2011-03-10 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.
Book Synopsis Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 by : Nicholas M. Katz
Download or read book Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2016-03-02 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.
