The Geometry of Moduli Spaces of Sheaves

The Geometry of Moduli Spaces of Sheaves
Author :
Publisher : Cambridge University Press
Total Pages : 345
Release :
ISBN-10 : 9781139485821
ISBN-13 : 1139485822
Rating : 4/5 (21 Downloads)

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

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.

Vector Bundles and Representation Theory

Vector Bundles and Representation Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 258
Release :
ISBN-10 : 9780821832646
ISBN-13 : 0821832646
Rating : 4/5 (46 Downloads)

Synopsis Vector Bundles and Representation Theory by : Steven Dale Cutkosky

This volume contains 13 papers from the conference on ``Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

Homological Mirror Symmetry and Tropical Geometry

Homological Mirror Symmetry and Tropical Geometry
Author :
Publisher : Springer
Total Pages : 445
Release :
ISBN-10 : 9783319065144
ISBN-13 : 3319065149
Rating : 4/5 (44 Downloads)

Synopsis Homological Mirror Symmetry and Tropical Geometry by : Ricardo Castano-Bernard

The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics
Author :
Publisher : Springer Science & Business Media
Total Pages : 435
Release :
ISBN-10 : 9780817646639
ISBN-13 : 0817646639
Rating : 4/5 (39 Downloads)

Synopsis Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics by : CLAUDIO BARTOCCI

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character. "Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph. Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index. This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.

String-Math 2011

String-Math 2011
Author :
Publisher : American Mathematical Soc.
Total Pages : 506
Release :
ISBN-10 : 9780821872956
ISBN-13 : 0821872958
Rating : 4/5 (56 Downloads)

Synopsis String-Math 2011 by : Jonathan Block

The nature of interactions between mathematicians and physicists has been thoroughly transformed in recent years. String theory and quantum field theory have contributed a series of profound ideas that gave rise to entirely new mathematical fields and revitalized older ones. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. A large and rapidly growing number of both mathematicians and physicists are working at the string-theoretic interface between the two academic fields. The String-Math conference series aims to bring together leading mathematicians and mathematically minded physicists working in this interface. This volume contains the proceedings of the inaugural conference in this series, String-Math 2011, which was held June 6-11, 2011, at the University of Pennsylvania.

Algebraic Geometry In East Asia, Proceedings Of The Symposium

Algebraic Geometry In East Asia, Proceedings Of The Symposium
Author :
Publisher : World Scientific
Total Pages : 273
Release :
ISBN-10 : 9789814486736
ISBN-13 : 9814486736
Rating : 4/5 (36 Downloads)

Synopsis Algebraic Geometry In East Asia, Proceedings Of The Symposium by : Kazuhiro Konno

This book is the proceedings of the conference “Algebraic Geometry in East Asia” which was held in International Institute for Advanced Studies (IIAS) during August 3 to August 10, 2001.As the breadth of the topics covered in this proceedings demonstrate, the conference was indeed successful in assembling a wide spectrum of East Asian mathematicians, and gave them a welcome chance to discuss current state of algebraic geometry.

Proceedings of the Symposium on Algebraic Geometry in East Asia

Proceedings of the Symposium on Algebraic Geometry in East Asia
Author :
Publisher : World Scientific
Total Pages : 280
Release :
ISBN-10 : 9812705104
ISBN-13 : 9789812705105
Rating : 4/5 (04 Downloads)

Synopsis Proceedings of the Symposium on Algebraic Geometry in East Asia by : Akira Ohbuchi

This book is the proceedings of the conference OC Algebraic Geometry in East AsiaOCO which was held in International Institute for Advanced Studies (IIAS) during August 3 to August 10, 2001.As the breadth of the topics covered in this proceedings demonstrate, the conference was indeed successful in assembling a wide spectrum of East Asian mathematicians, and gave them a welcome chance to discuss current state of algebraic geometry."

Moduli of Curves

Moduli of Curves
Author :
Publisher : Springer Science & Business Media
Total Pages : 381
Release :
ISBN-10 : 9780387227375
ISBN-13 : 0387227377
Rating : 4/5 (75 Downloads)

Synopsis Moduli of Curves by : Joe Harris

A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.

Mathematical Reviews

Mathematical Reviews
Author :
Publisher :
Total Pages : 984
Release :
ISBN-10 : UOM:39015067268261
ISBN-13 :
Rating : 4/5 (61 Downloads)

Synopsis Mathematical Reviews by :