Algebraic Varieties Minimal Models And Finite Generation PDF Download
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| Author | : Yujiro Kawamata |
| Publisher | : Cambridge University Press |
| Total Pages | : 263 |
| Release | : 2024-06-30 |
| Genre | : Mathematics |
| ISBN | : 1009344676 |
Download Algebraic Varieties: Minimal Models and Finite Generation Book in PDF, ePub and Kindle
The finite generation theorem is a major achievement of modern algebraic geometry. Based on the minimal model theory, it states that the canonical ring of an algebraic variety defined over a field of characteristic zero is a finitely generated graded ring. This graduate-level text is the first to explain this proof. It covers the progress on the minimal model theory over the last 30 years, culminating in the landmark paper on finite generation by Birkar-Cascini-Hacon-McKernan. Building up to this proof, the author presents important results and techniques that are now part of the standard toolbox of birational geometry, including Mori's bend and break method, vanishing theorems, positivity theorems and Siu's analysis on multiplier ideal sheaves. Assuming only the basics in algebraic geometry, the text keeps prerequisites to a minimum with self-contained explanations of terminology and theorems.
| Author | : Christopher D. Hacon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 206 |
| Release | : 2011-02-02 |
| Genre | : Mathematics |
| ISBN | : 3034602901 |
Download Classification of Higher Dimensional Algebraic Varieties Book in PDF, ePub and Kindle
Higher 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 | : Yves Félix |
| Publisher | : Oxford University Press |
| Total Pages | : 483 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0199206511 |
Download Algebraic Models in Geometry Book in PDF, ePub and Kindle
A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.
| Author | : Christopher D. Hacon |
| Publisher | : |
| Total Pages | : 208 |
| Release | : 2010 |
| Genre | : Geometry, Algebraic |
| ISBN | : 9781280391460 |
Download Classification of Higher Dimensional Algebraic Varieties: Compact moduli spaces of canonically polarized varieties Book in PDF, ePub and Kindle
This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on the existence of minimal models for varieties of log general type and of the finite generation of the canonical ring. The second part is an introduction to the theory of moduli spaces. It includes topics such as representing and moduli functors, Hilbert schemes, the boundedness, local closedness and separatedness of moduli spaces and the boundedness for varieties of general type. The book is aimed at advanced graduate students and researchers in algebraic geometry.
| Author | : Carel Faber |
| Publisher | : European Mathematical Society |
| Total Pages | : 356 |
| Release | : 2011 |
| Genre | : Algebraic varieties |
| ISBN | : 9783037190074 |
Download Classification of Algebraic Varieties Book in PDF, ePub and Kindle
Fascinating and surprising developments are taking place in the classification of algebraic varieties. The work of Hacon and McKernan and many others is causing a wave of breakthroughs in the minimal model program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony to the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.
| Author | : Adam Sheffer |
| Publisher | : Cambridge University Press |
| Total Pages | : 263 |
| Release | : 2022-03-24 |
| Genre | : Mathematics |
| ISBN | : 1108832490 |
Download Polynomial Methods and Incidence Theory Book in PDF, ePub and Kindle
A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.
| Author | : Gunter Malle |
| Publisher | : Cambridge University Press |
| Total Pages | : 324 |
| Release | : 2011-09-08 |
| Genre | : Mathematics |
| ISBN | : 113949953X |
Download Linear Algebraic Groups and Finite Groups of Lie Type Book in PDF, ePub and Kindle
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
| Author | : Spencer Bloch |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 489 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : 0821814761 |
Download Algebraic Geometry Book in PDF, ePub and Kindle
| Author | : Kunihiko Kodaira |
| Publisher | : CUP Archive |
| Total Pages | : 424 |
| Release | : 1977 |
| Genre | : Mathematics |
| ISBN | : 9780521217774 |
Download Complex Analysis and Algebraic Geometry Book in PDF, ePub and Kindle
The 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 | : Ravi Vakil |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 202 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821837192 |
Download Snowbird Lectures in Algebraic Geometry Book in PDF, ePub and Kindle
A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry. The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.
