Moduli Theory And Classification Theory Of Algebraic Varieties
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Author |
: H. Popp |
Publisher |
: Springer |
Total Pages |
: 196 |
Release |
: 2006-11-15 |
ISBN-10 |
: 9783540370314 |
ISBN-13 |
: 3540370315 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Moduli Theory and Classification Theory of Algebraic Varieties by : H. Popp
Author |
: Herbert Popp |
Publisher |
: |
Total Pages |
: |
Release |
: 1977 |
ISBN-10 |
: OCLC:472120227 |
ISBN-13 |
: |
Rating |
: 4/5 (27 Downloads) |
Synopsis Moduli theory and classification theory of algebraic varieties by : Herbert Popp
Author |
: K. Ueno |
Publisher |
: Springer |
Total Pages |
: 296 |
Release |
: 2006-11-15 |
ISBN-10 |
: 9783540374152 |
ISBN-13 |
: 3540374159 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Classification Theory of Algebraic Varieties and Compact Complex Spaces by : K. Ueno
Author |
: Christopher D. Hacon |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 206 |
Release |
: 2011-02-02 |
ISBN-10 |
: 9783034602907 |
ISBN-13 |
: 3034602901 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Classification of Higher Dimensional Algebraic Varieties by : Christopher D. Hacon
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 |
: Kenji Ueno |
Publisher |
: Springer |
Total Pages |
: 278 |
Release |
: 1975-01-01 |
ISBN-10 |
: 0387071385 |
ISBN-13 |
: 9780387071381 |
Rating |
: 4/5 (85 Downloads) |
Synopsis Classification Theory of Algebraic Varieties and Compact Complex Spaces by : Kenji Ueno
Author |
: Kenji Ueno |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 328 |
Release |
: 2002 |
ISBN-10 |
: 0821821563 |
ISBN-13 |
: 9780821821565 |
Rating |
: 4/5 (63 Downloads) |
Synopsis Advances in Moduli Theory by : Kenji Ueno
The word ``moduli'' in the sense of this book first appeared in the epoch-making paper of B. Riemann, Theorie der Abel'schen Funktionen, published in 1857. Riemann defined a Riemann surface of an algebraic function field as a branched covering of a one-dimensional complex projective space, and found out that Riemann surfaces have parameters. This work gave birth to the theory of moduli. However, the viewpoint regarding a Riemann surface as an algebraic curve became the mainstream,and the moduli meant the parameters for the figures (graphs) defined by equations. In 1913, H. Weyl defined a Riemann surface as a complex manifold of dimension one. Moreover, Teichmuller's theory of quasiconformal mappings and Teichmuller spaces made a start for new development of the theory ofmoduli, making possible a complex analytic approach toward the theory of moduli of Riemann surfaces. This theory was then investigated and made complete by Ahlfors, Bers, Rauch, and others. However, the theory of Teichmuller spaces utilized the special nature of complex dimension one, and it was difficult to generalize it to an arbitrary dimension in a direct way. It was Kodaira-Spencer's deformation theory of complex manifolds that allowed one to study arbitrary dimensional complex manifolds.Initial motivation in Kodaira-Spencer's discussion was the need to clarify what one should mean by number of moduli. Their results, together with further work by Kuranishi, provided this notion with intrinsic meaning. This book begins by presenting the Kodaira-Spencer theory in its original naiveform in Chapter 1 and introduces readers to moduli theory from the viewpoint of complex analytic geometry. Chapter 2 briefly outlines the theory of period mapping and Jacobian variety for compact Riemann surfaces, with the Torelli theorem as a goal. The theory of period mappings for compact Riemann surfaces can be generalized to the theory of period mappings in terms of Hodge structures for compact Kahler manifolds. In Chapter 3, the authors state the theory of Hodge structures, focusingbriefly on period mappings. Chapter 4 explains conformal field theory as an application of moduli theory. This is the English translation of a book originally published in Japanese. Other books by Kenji Ueno published in this AMS series, Translations of Mathematical Monographs, include An Introduction toAlgebraic Geometry, Volume 166, Algebraic Geometry 1: From Algebraic Varieties to Schemes, Volume 185, and Algebraic Geometry 2: Sheaves and Cohomology, Volume 197.
Author |
: Christopher D. Hacon |
Publisher |
: |
Total Pages |
: 208 |
Release |
: 2010 |
ISBN-10 |
: 1280391464 |
ISBN-13 |
: 9781280391460 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Classification of Higher Dimensional Algebraic Varieties: Compact moduli spaces of canonically polarized varieties by : Christopher D. Hacon
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 |
: Piotr Pragacz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 321 |
Release |
: 2006-03-30 |
ISBN-10 |
: 9783764373429 |
ISBN-13 |
: 3764373423 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Topics in Cohomological Studies of Algebraic Varieties by : Piotr Pragacz
The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis
Author |
: Paola Comparin |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 282 |
Release |
: 2021-04-23 |
ISBN-10 |
: 9781470453275 |
ISBN-13 |
: 1470453274 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties by : Paola Comparin
Articles in this volume are based on lectures given at three conferences on Geometry at the Frontier, held at the Universidad de la Frontera, Pucón, Chile in 2016, 2017, and 2018. The papers cover recent developments on the theory of algebraic varieties—in particular, of their automorphism groups and moduli spaces. They will be of interest to anyone working in the area, as well as young mathematicians and students interested in complex and algebraic geometry.
Author |
: Ciro Ciliberto |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 434 |
Release |
: 1994 |
ISBN-10 |
: 9780821851791 |
ISBN-13 |
: 0821851799 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Classification of Algebraic Varieties by : Ciro Ciliberto
This volume contains the proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, held in May 1992 at the University of L'Aquila in Italy. The papers discuss a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered are algebraic curve theory, algebraic surface theory, the theory of minimal models, braid groups and the topology of algebraic varieties, toric varieties. In addition to algebraic geometers, theoretical physicists in some areas will find this book useful. The book is also suitable for an advanced graduate course in algebraic geometry, as it provides an overview of areas of current research.