Donaldson Type Invariants For Algebraic Surfaces
DOWNLOAD eBooks
Download Donaldson Type Invariants For Algebraic Surfaces PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Donaldson Type Invariants For Algebraic Surfaces book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Donaldson Type Invariants For Algebraic Surfaces
DOWNLOAD eBooks
Author : Takuro Mochizuki
language : en
Publisher: Springer
Release Date : 2009-04-20
Donaldson Type Invariants For Algebraic Surfaces written by Takuro Mochizuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Mathematics categories.
In this monograph, we de?ne and investigate an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We may expect the existence of interesting “universal relations among invariants”, which would be a natural generalization of the “wall-crossing formula” and the “Witten conjecture” for classical Donaldson invariants. Our goal is to obtain a weaker version of such relations, in other brief words, to describe a relation as the sum of integrals over the products of m- uli spaces of objects with lower ranks. Fortunately, according to a recent excellent work of L. Gottsche, ̈ H. Nakajima and K. Yoshioka, [53], a wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case. We hope that our work in this monograph would, at least tentatively, provides a part of foundation for the further study on such universal relations. In the rest of this preface, we would like to explain our motivation and some of important ingredients of this study. See Introduction for our actual problems and results. Donaldson Invariants Let us brie?y recall Donaldson invariants. We refer to [22] for more details and precise. We also refer to [37], [39], [51] and [53]. LetX be a compact simply con- ? nected oriented real 4-dimensional C -manifold with a Riemannian metric g. Let P be a principalSO(3)-bundle on X.
An So 3 Monopole Cobordism Formula Relating Donaldson And Seiberg Witten Invariants
DOWNLOAD eBooks
Author : Paul Feehan
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-08
An So 3 Monopole Cobordism Formula Relating Donaldson And Seiberg Witten Invariants written by Paul Feehan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Cobordism theory categories.
The authors prove an analogue of the Kotschick–Morgan Conjecture in the context of monopoles, obtaining a formula relating the Donaldson and Seiberg–Witten invariants of smooth four-manifolds using the -monopole cobordism. The main technical difficulty in the -monopole program relating the Seiberg–Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible monopoles, namely the moduli spaces of Seiberg–Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of monopoles. In this monograph, the authors prove—modulo a gluing theorem which is an extension of their earlier work—that these intersection pairings can be expressed in terms of topological data and Seiberg–Witten invariants of the four-manifold. Their proofs that the -monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Mariño, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with and odd appear in earlier works.
Recent Progress On The Donaldson Thomas Theory
DOWNLOAD eBooks
Author : Yukinobu Toda
language : en
Publisher: Springer Nature
Release Date : 2021-12-15
Recent Progress On The Donaldson Thomas Theory written by Yukinobu Toda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-15 with Science categories.
This book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi–Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov–Witten/Donaldson–Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others. Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi–Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar–Vafa invariant, which was first proposed by Gopakumar–Vafa in 1998, but its precise mathematical definition has not been available until recently. This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.
Algebraic Surfaces
DOWNLOAD eBooks
Author : Lucian Badescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-02-08
Algebraic Surfaces written by Lucian Badescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-08 with Mathematics categories.
This book presents fundamentals from the theory of algebraic surfaces, including areas such as rational singularities of surfaces and their relation with Grothendieck duality theory, numerical criteria for contractibility of curves on an algebraic surface, and the problem of minimal models of surfaces. In fact, the classification of surfaces is the main scope of this book and the author presents the approach developed by Mumford and Bombieri. Chapters also cover the Zariski decomposition of effective divisors and graded algebras.
Mirror Symmetry And Tropical Geometry
DOWNLOAD eBooks
Author : Ricardo Castaño-Bernard
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Mirror Symmetry And Tropical Geometry written by Ricardo Castaño-Bernard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Algebraic varieties categories.
This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. --
Compact Moduli Spaces And Vector Bundles
DOWNLOAD eBooks
Author : Valery Alexeev
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Compact Moduli Spaces And Vector Bundles written by Valery Alexeev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.
Algebraic Geometry Santa Cruz 1995
DOWNLOAD eBooks
Author : János Kollár
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Algebraic Geometry Santa Cruz 1995 written by János Kollár and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Geometry, Algebraic categories.
Computational Approach To Riemann Surfaces
DOWNLOAD eBooks
Author : Alexander I. Bobenko TU Berlin
language : en
Publisher: Springer
Release Date : 2011-02-03
Computational Approach To Riemann Surfaces written by Alexander I. Bobenko TU Berlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-03 with Mathematics categories.
This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.
Symmetries Of Compact Riemann Surfaces
DOWNLOAD eBooks
Author : Emilio Bujalance
language : en
Publisher: Springer
Release Date : 2010-09-29
Symmetries Of Compact Riemann Surfaces written by Emilio Bujalance and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-29 with Mathematics categories.
This monograph covers symmetries of compact Riemann surfaces. It examines the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.
Topics In Algebraic And Topological K Theory
DOWNLOAD eBooks
Author : Paul Frank Baum
language : en
Publisher: Springer
Release Date : 2010-10-28
Topics In Algebraic And Topological K Theory written by Paul Frank Baum and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-28 with Mathematics categories.
This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.