Compact Moduli Spaces and Vector Bundles

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Publisher : American Mathematical Soc.
ISBN 13 : 0821868993
Total Pages : 264 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Compact Moduli Spaces and Vector Bundles by : Valery Alexeev

Download or read book Compact Moduli Spaces and Vector Bundles written by Valery Alexeev and published by American Mathematical Soc.. This book was released on 2012 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia. This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks. Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves. The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.

Compact Moduli Spaces and Vector Bundles

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821889540
Total Pages : 264 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Compact Moduli Spaces and Vector Bundles by : Valery Alexeev

Download or read book Compact Moduli Spaces and Vector Bundles written by Valery Alexeev and published by American Mathematical Soc.. This book was released on 2012 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Moduli Spaces and Vector Bundles

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Publisher : Cambridge University Press
ISBN 13 : 0521734711
Total Pages : 516 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Moduli Spaces and Vector Bundles by : Steve Bradlow

Download or read book Moduli Spaces and Vector Bundles written by Steve Bradlow and published by Cambridge University Press. This book was released on 2009-05-21 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Compactifying Moduli Spaces

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Publisher : Birkhäuser
ISBN 13 : 3034809212
Total Pages : 135 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Compactifying Moduli Spaces by : Paul Hacking

Download or read book Compactifying Moduli Spaces written by Paul Hacking and published by Birkhäuser. This book was released on 2016-02-04 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Curves

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Publisher : Springer
ISBN 13 : 3030029433
Total Pages : 231 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Algebraic Curves by : Maxim E. Kazaryan

Download or read book Algebraic Curves written by Maxim E. Kazaryan and published by Springer. This book was released on 2019-01-21 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Globally Generated Vector Bundles with Small C1 on Projective Spaces

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 1470428385
Total Pages : 107 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Globally Generated Vector Bundles with Small C1 on Projective Spaces by : Cristian Anghel

Download or read book Globally Generated Vector Bundles with Small C1 on Projective Spaces written by Cristian Anghel and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Vector Bundles

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Publisher : Cambridge University Press
ISBN 13 : 9780521481823
Total Pages : 260 pages
Book Rating : 4.4/5 (818 download)

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Book Synopsis Lectures on Vector Bundles by : J. Le Potier

Download or read book Lectures on Vector Bundles written by J. Le Potier and published by Cambridge University Press. This book was released on 1997-01-28 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and construction ideas in the general context of projective algebraic surfaces. Professor Le Potier provides a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Moduli Spaces and Vector Bundles

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Publisher :
ISBN 13 : 9781470472962
Total Pages : 0 pages
Book Rating : 4.4/5 (729 download)

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Book Synopsis Moduli Spaces and Vector Bundles by : Peter Beier Gothen

Download or read book Moduli Spaces and Vector Bundles written by Peter Beier Gothen and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytic and Algebraic Geometry

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Publisher : Springer
ISBN 13 : 981105648X
Total Pages : 292 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Analytic and Algebraic Geometry by : Anilatmaja Aryasomayajula

Download or read book Analytic and Algebraic Geometry written by Anilatmaja Aryasomayajula and published by Springer. This book was released on 2017-09-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Holomorphic Vector Bundles over Compact Complex Surfaces

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Publisher : Springer
ISBN 13 : 3540498451
Total Pages : 175 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Holomorphic Vector Bundles over Compact Complex Surfaces by : Vasile Brinzanescu

Download or read book Holomorphic Vector Bundles over Compact Complex Surfaces written by Vasile Brinzanescu and published by Springer. This book was released on 2006-11-14 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry.

Moduli of Vector Bundles

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Publisher : CRC Press
ISBN 13 : 9780824797386
Total Pages : 324 pages
Book Rating : 4.7/5 (973 download)

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Book Synopsis Moduli of Vector Bundles by : Masaki Maruyama

Download or read book Moduli of Vector Bundles written by Masaki Maruyama and published by CRC Press. This book was released on 1996-04-23 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains papers presented at the 35th Taniguchi International Symposium held recently in Sanda and Kyoto, Japan. Details the latest developments concerning moduli spaces of vector bundles or instantons and their application. Covers a broad array of topics in both differential and algebraic geometry."

Grassmannians, Moduli Spaces and Vector Bundles

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Publisher : American Mathematical Soc.
ISBN 13 : 0821852051
Total Pages : 190 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Grassmannians, Moduli Spaces and Vector Bundles by : David Ellwood

Download or read book Grassmannians, Moduli Spaces and Vector Bundles written by David Ellwood and published by American Mathematical Soc.. This book was released on 2011 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Vector Bundles

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Publisher : Universitätsverlag Göttingen
ISBN 13 : 3938616741
Total Pages : 330 pages
Book Rating : 4.9/5 (386 download)

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Book Synopsis Vector Bundles by : Andrej N. Tjurin

Download or read book Vector Bundles written by Andrej N. Tjurin and published by Universitätsverlag Göttingen. This book was released on 2008 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a three volume collection of Andrey Nikolaevich Tyurin's Selected Works. It includes his most interesting articles in the field of classical algebraic geometry, written during his whole career from the 1960s. Most of these papers treat different problems of the theory of vector bundles on curves and higher dimensional algebraic varieties, a theory which is central to algebraic geometry and most of its applications.

Differential Geometry of Complex Vector Bundles

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Publisher : Princeton University Press
ISBN 13 : 1400858682
Total Pages : 317 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Differential Geometry of Complex Vector Bundles by : Shoshichi Kobayashi

Download or read book Differential Geometry of Complex Vector Bundles written by Shoshichi Kobayashi and published by Princeton University Press. This book was released on 2014-07-14 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Vector Bundles on Complex Projective Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 1475714602
Total Pages : 389 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Vector Bundles on Complex Projective Spaces by : Christian Okonek

Download or read book Vector Bundles on Complex Projective Spaces written by Christian Okonek and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are intended as an introduction to the methods of classification of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = Fn. According to Serre (GAGA) the classification of holomorphic vector bundles is equivalent to the classification of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some funda mental results from these fields are summarized at the beginning. One of the authors gave a survey in the Seminaire Bourbaki 1978 on the current state of the classification of holomorphic vector bundles overFn. This lecture then served as the basis for a course of lectures in Gottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the introductory nature of this book we have had to leave out some difficult topics such as the restriction theorem of Barth. As compensation we have appended to each sec tion a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of paragraphs. Each section is preceeded by a short description of iv its contents.

The Geometry of Moduli Spaces of Sheaves

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Publisher : Cambridge University Press
ISBN 13 : 1139485822
Total Pages : 345 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts

Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

On the Compactification of Moduli Spaces for Algebraic $K3$ Surfaces

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Publisher : American Mathematical Soc.
ISBN 13 : 0821824376
Total Pages : 86 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On the Compactification of Moduli Spaces for Algebraic $K3$ Surfaces by : Francesco Scattone

Download or read book On the Compactification of Moduli Spaces for Algebraic $K3$ Surfaces written by Francesco Scattone and published by American Mathematical Soc.. This book was released on 1987 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: