Compactifying Moduli Spaces For Abelian Varieties

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Compactifying Moduli Spaces for Abelian Varieties

Martin C. Olsson
Compactifying Moduli Spaces for Abelian Varieties Book PDF

Author : Martin C. Olsson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 53,7 Mb
Release : 2008-08-25
Category : Mathematics
ISBN : 9783540705185

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Compactifying Moduli Spaces for Abelian Varieties by Martin C. Olsson Pdf

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.

Moduli Spaces of Abelian Surfaces

Klaus Hulek,Constantin Kahn,Steven H. Weintraub
Moduli Spaces of Abelian Surfaces Book PDF

Author : Klaus Hulek,Constantin Kahn,Steven H. Weintraub
Publisher : Walter de Gruyter
Page : 361 pages
File Size : 41,7 Mb
Release : 2011-05-03
Category : Mathematics
ISBN : 9783110891928

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Moduli Spaces of Abelian Surfaces by Klaus Hulek,Constantin Kahn,Steven H. Weintraub Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Compactifying Moduli Spaces

Paul Hacking,Radu Laza,Dragos Oprea
Compactifying Moduli Spaces Book PDF

Author : Paul Hacking,Radu Laza,Dragos Oprea
Publisher : Birkhäuser
Page : 135 pages
File Size : 51,5 Mb
Release : 2016-02-04
Category : Mathematics
ISBN : 9783034809214

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Compactifying Moduli Spaces by Paul Hacking,Radu Laza,Dragos Oprea Pdf

This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps. Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.

Moduli of Abelian Varieties

Gerard van der Geer,C. Faber,Frans Oort
Moduli of Abelian Varieties Book PDF

Author : Gerard van der Geer,C. Faber,Frans Oort
Publisher : Birkhäuser
Page : 526 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883030

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Moduli of Abelian Varieties by Gerard van der Geer,C. Faber,Frans Oort Pdf

Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

Surveys on Recent Developments in Algebraic Geometry

Izzet Coskun,Tommaso de Fernex,Angela Gibney
Surveys on Recent Developments in Algebraic Geometry Book PDF

Author : Izzet Coskun,Tommaso de Fernex,Angela Gibney
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 46,6 Mb
Release : 2017-07-12
Category : $K$-theory -- Higher algebraic $K$-theory -- $Q$- and plus-constructions
ISBN : 9781470435578

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Surveys on Recent Developments in Algebraic Geometry by Izzet Coskun,Tommaso de Fernex,Angela Gibney Pdf

The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.

A Celebration of Algebraic Geometry

Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil
A Celebration of Algebraic Geometry Book PDF

Author : Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil
Publisher : American Mathematical Soc.
Page : 614 pages
File Size : 44,7 Mb
Release : 2013-09-11
Category : Mathematics
ISBN : 9780821889831

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A Celebration of Algebraic Geometry by Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil Pdf

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Current Developments in Algebraic Geometry

Lucia Caporaso
Current Developments in Algebraic Geometry Book PDF

Author : Lucia Caporaso
Publisher : Cambridge University Press
Page : 437 pages
File Size : 53,9 Mb
Release : 2012-03-19
Category : Mathematics
ISBN : 9780521768252

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Current Developments in Algebraic Geometry by Lucia Caporaso Pdf

This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.

Selected Papers

David Mumford
Selected Papers Book PDF

Author : David Mumford
Publisher : Springer Science & Business Media
Page : 834 pages
File Size : 44,9 Mb
Release : 2004-07-15
Category : Mathematics
ISBN : 038721092X

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Selected Papers by David Mumford Pdf

Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics. Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.

Encyclopaedia of Mathematics

Michiel Hazewinkel
Encyclopaedia of Mathematics Book PDF

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 48,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400959910

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Encyclopaedia of Mathematics (set)

Michiel Hazewinkel
Encyclopaedia of Mathematics set Book PDF

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 982 pages
File Size : 48,8 Mb
Release : 1994-02-28
Category : Mathematics
ISBN : 1556080107

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Encyclopaedia of Mathematics (set) by Michiel Hazewinkel Pdf

The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.

Fifth International Congress of Chinese Mathematicians

Lizhen Ji
Fifth International Congress of Chinese Mathematicians Book PDF

Author : Lizhen Ji
Publisher : American Mathematical Soc.
Page : 520 pages
File Size : 46,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821875865

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Fifth International Congress of Chinese Mathematicians by Lizhen Ji Pdf

This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.

Moduli of Abelian Varieties

Gerard van der Geer,C. Faber,Frans Oort
Moduli of Abelian Varieties Book PDF

Author : Gerard van der Geer,C. Faber,Frans Oort
Publisher : Birkhäuser
Page : 518 pages
File Size : 52,5 Mb
Release : 2012-10-23
Category : Mathematics
ISBN : 3034895097

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Moduli of Abelian Varieties by Gerard van der Geer,C. Faber,Frans Oort Pdf

Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

Recent Topics in Differential and Analytic Geometry

T. Ochiai
Recent Topics in Differential and Analytic Geometry Book PDF

Author : T. Ochiai
Publisher : Academic Press
Page : 462 pages
File Size : 48,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781483214689

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Recent Topics in Differential and Analytic Geometry by T. Ochiai Pdf

Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains. Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind. This book is a valuable resource for graduate students and pure mathematicians.

Curves and Abelian Varieties

Valery Alexeev,Arnaud Beauville,Charles Herbert Clemens,Elham Izadi
Curves and Abelian Varieties Book PDF

Author : Valery Alexeev,Arnaud Beauville,Charles Herbert Clemens,Elham Izadi
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 53,5 Mb
Release : 2008
Category : Abelian varieties
ISBN : 9780821843345

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Curves and Abelian Varieties by Valery Alexeev,Arnaud Beauville,Charles Herbert Clemens,Elham Izadi Pdf

"This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes." "In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors. of compactified Jucobiuns of singular curves, and of "strange duality" among moduli spaces of vector bundles on algebraic varieties."--BOOK JACKET.

Degeneration of Abelian Varieties

Gerd Faltings,Ching-Li Chai
Degeneration of Abelian Varieties Book PDF

Author : Gerd Faltings,Ching-Li Chai
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 41,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662026328

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Degeneration of Abelian Varieties by Gerd Faltings,Ching-Li Chai Pdf

A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.