Algebraic Varieties: Minimal Models and Finite Generation PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Algebraic Varieties: Minimal Models and Finite Generation PDF full book. Access full book title Algebraic Varieties: Minimal Models and Finite Generation by Yujiro Kawamata. Download full books in PDF and EPUB format.
Author: Yujiro Kawamata
Publisher: Cambridge University Press
ISBN: 1009344676
Category : Mathematics
Languages : en
Pages : 263
Get Book Here
Book Description
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: Yujiro Kawamata
Publisher: Cambridge University Press
ISBN: 1009344676
Category : Mathematics
Languages : en
Pages : 263
Get Book Here
Book Description
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
ISBN: 3034602901
Category : Mathematics
Languages : en
Pages : 206
Get Book Here
Book Description
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: Christopher D. Hacon
Publisher:
ISBN: 9781280391460
Category : Geometry, Algebraic
Languages : en
Pages : 208
Get Book Here
Book Description
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
ISBN: 9783037190074
Category : Algebraic varieties
Languages : en
Pages : 356
Get Book Here
Book Description
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
ISBN: 1108832490
Category : Mathematics
Languages : en
Pages : 263
Get Book Here
Book Description
A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.
Author: Arnaud Beauville
Publisher: Cambridge University Press
ISBN: 9780521498425
Category : Mathematics
Languages : en
Pages : 148
Get Book Here
Book Description
Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor BeauviIle gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.
Author: Spencer Bloch
Publisher: American Mathematical Soc.
ISBN: 0821814761
Category : Mathematics
Languages : en
Pages : 489
Get Book Here
Book Description
Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Category : Mathematics
Languages : en
Pages : 180
Get Book Here
Book Description
An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.
Author: Gunter Malle
Publisher: Cambridge University Press
ISBN: 113949953X
Category : Mathematics
Languages : en
Pages : 324
Get Book Here
Book Description
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: Ravi Vakil
Publisher: American Mathematical Soc.
ISBN: 0821837192
Category : Mathematics
Languages : en
Pages : 202
Get Book Here
Book Description
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.
