Compactifying Moduli Spaces

Author : Paul Hacking,Radu Laza,Dragos Oprea
Publisher : Birkhäuser
Page : 135 pages
File Size : 47,7 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.

Author : Martin C. Olsson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 41,9 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.

Author : Francesco Scattone
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 53,7 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821824375

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On the Compactification of Moduli Spaces for Algebraic $K3$ Surfaces by Francesco Scattone Pdf

Author : Klaus Hulek,Constantin Kahn,Steven H. Weintraub
Publisher : Walter de Gruyter
Page : 361 pages
File Size : 48,8 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)

Author : David Ellwood,Emma Previato
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 45,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852057

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Grassmannians, Moduli Spaces and Vector Bundles by David Ellwood,Emma Previato Pdf

This collection of cutting-edge articles on vector bundles and related topics originated from a CMI workshop, held in October 2006, that brought together a community indebted to the pioneering work of P. E. Newstead, visiting the United States for the first time since the 1960s. Moduli spaces of vector bundles were then in their infancy, but are now, as demonstrated by this volume, a powerful tool in symplectic geometry, number theory, mathematical physics, and algebraic geometry. In fact, the impetus for this volume was to offer a sample of the vital convergence of techniques and fundamental progress, taking place in moduli spaces at the outset of the twenty-first century. This volume contains contributions by J. E. Andersen and N. L. Gammelgaard (Hitchin's projectively flat connection and Toeplitz operators), M. Aprodu and G. Farkas (moduli spaces), D. Arcara and A. Bertram (stability in higher dimension), L. Jeffrey (intersection cohomology), J. Kamnitzer (Langlands program), M. Lieblich (arithmetic aspects), P. E. Newstead (coherent systems), G. Pareschi and M. Popa (linear series on Abelian varieties), and M. Teixidor i Bigas (bundles over reducible curves). These articles do require a working knowledge of algebraic geometry, symplectic geometry and functional analysis, but should appeal to practitioners in a diversity of fields. No specialization should be necessary to appreciate the contributions, or possibly to be stimulated to work in the various directions opened by these path-blazing ideas; to mention a few, the Langlands program, stability criteria for vector bundles over surfaces and threefolds, linear series over abelian varieties and Brauer groups in relation to arithmetic properties of moduli spaces.

Author : Vladimir Fock,Andrey Marshakov,Florent Schaffhauser,Constantin Teleman,Richard Wentworth
Publisher : Birkhäuser
Page : 220 pages
File Size : 43,7 Mb
Release : 2016-12-25
Category : Mathematics
ISBN : 9783319335780

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Geometry and Quantization of Moduli Spaces by Vladimir Fock,Andrey Marshakov,Florent Schaffhauser,Constantin Teleman,Richard Wentworth Pdf

This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.

Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 42,7 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897

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Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo Pdf

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Author : Valery Alexeev
Publisher : Birkhäuser
Page : 104 pages
File Size : 44,5 Mb
Release : 2015-05-18
Category : Mathematics
ISBN : 9783034809153

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Moduli of Weighted Hyperplane Arrangements by Valery Alexeev Pdf

This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory – to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification techniques for moduli spaces in a large class where computations are possible, namely that of weighted stable hyperplane arrangements (shas).

Author : Anilatmaja Aryasomayajula,Indranil Biswas,Archana S. Morye,A. J. Parameswaran
Publisher : Springer
Page : 292 pages
File Size : 51,9 Mb
Release : 2017-09-08
Category : Mathematics
ISBN : 9789811056482

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Analytic and Algebraic Geometry by Anilatmaja Aryasomayajula,Indranil Biswas,Archana S. Morye,A. J. Parameswaran Pdf

This volume is an outcome of the International conference held in Tata Institute of Fundamental Research and the University of Hyderabad. There are fifteen articles in this volume. The main purpose of the articles is to introduce recent and advanced techniques in the area of analytic and algebraic geometry. This volume attempts to give recent developments in the area to target mainly young researchers who are new to this area. Also, some research articles have been added to give examples of how to use these techniques to prove new results.

Author : Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov
Publisher : Springer
Page : 231 pages
File Size : 42,8 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030029432

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Algebraic Curves by Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov Pdf

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework

Author : Owen Biesel,David Holmes
Publisher : American Mathematical Society
Page : 104 pages
File Size : 41,6 Mb
Release : 2023-05-23
Category : Mathematics
ISBN : 9781470463106

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Fine Compactified Moduli of Enriched Structures on Stable Curves by Owen Biesel,David Holmes Pdf

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Author : Venkatrama Lakshmibai,V. Balaji,V. B. Mehta,K. R. Nagarajan,K. Paranjape,P. Sankaran,R. Sridharan
Publisher : Springer Science & Business Media
Page : 598 pages
File Size : 55,7 Mb
Release : 2003-07-24
Category : Mathematics
ISBN : 3764304448

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A Tribute to C.S. Seshadri by Venkatrama Lakshmibai,V. Balaji,V. B. Mehta,K. R. Nagarajan,K. Paranjape,P. Sankaran,R. Sridharan Pdf

C.S. Seshadri turned seventy on the 29th of February, 2002. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri's contributions to mathematics. This volume includes expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference for researchers and students in these areas.

Author : T. Ochiai
Publisher : Academic Press
Page : 462 pages
File Size : 44,9 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.

Author : Brian Greene,Costas Efthimiou
Publisher : World Scientific
Page : 1089 pages
File Size : 45,9 Mb
Release : 1997-08-01
Category : Electronic
ISBN : 9789814546119

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Fields, Strings And Duality (Tasi 1996) by Brian Greene,Costas Efthimiou Pdf

The past year has witnessed truly remarkable developments in our understanding of string theory. Fields, Strings and Duality — TASI 96 is an invaluable collection of review papers on the subject, contributed by the most prominent researchers in the field. This volume is a scientific treasure for graduate students, researchers and all others who are interested in the progress of theoretical physics.

Author : K. Shiohama
Publisher : Elsevier
Page : 517 pages
File Size : 42,7 Mb
Release : 1989-10-04
Category : Mathematics
ISBN : 9780080925783

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Geometry of Manifolds by K. Shiohama Pdf

This volume contains the papers presented at a symposium on differential geometry at Shinshu University in July of 1988. Carefully reviewed by a panel of experts, the papers pertain to the following areas of research: dynamical systems, geometry of submanifolds and tensor geometry, lie sphere geometry, Riemannian geometry, Yang-Mills Connections, and geometry of the Laplace operator.