[PDF] Classification Of Higher Dimensional Algebraic Varieties Compact Moduli Spaces Of Canonically Polarized Varieties eBook

Author : Christopher D. Hacon
Publisher :
Page : 208 pages
File Size : 26,99 MB
Release : 2010
Category : Geometry, Algebraic
ISBN : 9781280391460

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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 : Christopher D. Hacon
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 49,33 MB
Release : 2011-02-02
Category : Mathematics
ISBN : 3034602901

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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 : Károly Jr. Böröczky
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 19,28 MB
Release : 2013-12-11
Category : Mathematics
ISBN : 3662051230

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Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

Author : Takao Fujita
Publisher : Cambridge University Press
Page : 223 pages
File Size : 28,28 MB
Release : 1990
Category : Algebraic varieties
ISBN : 0521392020

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A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or sur.

Author : Martin C. Olsson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 22,49 MB
Release : 2008-08-25
Category : Mathematics
ISBN : 354070518X

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This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.

Author : Carel Faber
Publisher : European Mathematical Society
Page : 356 pages
File Size : 23,49 MB
Release : 2011
Category : Algebraic varieties
ISBN : 9783037190074

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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.