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Author: János Kollár
Publisher: Cambridge University Press
Published: 2023-04-30
Total Pages: 491
ISBN-13: 1009346105
DOWNLOAD EBOOKThe first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.
Author: Tommaso de Fernex
Publisher: American Mathematical Soc.
Published: 2018-06-01
Total Pages: 674
ISBN-13: 1470435772
DOWNLOAD EBOOKThis 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.
Author: Christopher D. Hacon
Publisher: Springer Science & Business Media
Published: 2011-02-02
Total Pages: 206
ISBN-13: 3034602901
DOWNLOAD EBOOKHigher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
Author: Canadian Number Theory Association. Conference
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 426
ISBN-13: 0821809644
DOWNLOAD EBOOKThis book contains papers presented at the Fifth Canadian Number Theory Association (CNTA) conference held at Carleton University Ottawa, Ontario. The invited speakers focused on arithmetic algebraic geometry and elliptic curves, diophantine problems, analytic number theory, and algebraic and computational number theory. The contributed talks represented a wide variety of areas in number theory. David Boyd gave an hour-long talk on Mahler's Measure and Elliptic Curves. This lecture was open to the public and attracted a large audience from outside the conference.
Author: Kunihiko Kodaira
Publisher: Springer Nature
Published: 2020-09-17
Total Pages: 86
ISBN-13: 9811573808
DOWNLOAD EBOOKThis is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for curves on a surface and Noether's formula for the arithmetic genus. It also discusses the behavior of the pluri-canonical maps of surfaces of general type as a practical application of the general theory. The book is aimed at graduate students and also at anyone interested in algebraic surfaces, and readers are expected to have only a basic knowledge of complex manifolds as a prerequisite.
Author: Kunihiko Kodaira
Publisher: CUP Archive
Published: 1977
Total Pages: 424
ISBN-13: 9780521217774
DOWNLOAD EBOOKThe articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.
Author: Dan Abramovich
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 539
ISBN-13: 0821847031
DOWNLOAD EBOOKOffers 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.
Author: Yasuyuki Kachi
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 186
ISBN-13: 0821834010
DOWNLOAD EBOOKThis proceedings volume resulted from the John H. Barrett Memorial Lecture Series held at the University of Tennessee (Knoxville). The articles reflect recent developments in algebraic geometry. It is suitable for graduate students and researchers interested in algebra and algebraic geometry.
Author: János Kollár
Publisher: Cambridge University Press
Published: 2023-04-20
Total Pages: 492
ISBN-13: 1009346148
DOWNLOAD EBOOKThis book establishes the moduli theory of stable varieties, giving the optimal approach to understanding families of varieties of general type. Starting from the Deligne–Mumford theory of the moduli of curves and using Mori's program as a main tool, the book develops the techniques necessary for a theory in all dimensions. The main results give all the expected general properties, including a projective coarse moduli space. A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.
Author: Bjorn Poonen
Publisher: American Mathematical Soc.
Published: 2017-12-13
Total Pages: 358
ISBN-13: 1470437732
DOWNLOAD EBOOKThis book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
