Lectures On Hilbert Schemes Of Points On Surfaces
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Lectures On Hilbert Schemes Of Points On Surfaces
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Author : Hiraku Nakajima
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Lectures On Hilbert Schemes Of Points On Surfaces written by Hiraku Nakajima 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 1999 with Mathematics categories.
It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.
Qu Mian Shang Dian De Hilbert Gai Xing Jiang Yi
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Author : 中岛平 (日)
language : en
Publisher:
Release Date : 2018
Qu Mian Shang Dian De Hilbert Gai Xing Jiang Yi written by 中岛平 (日) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
本书为英文本,书中的讨论反映了Hilbert概形这方面的特性.
Extension Groups Of Tautological Sheaves On Hilbert Schemes Of Points On Surfaces
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Author : Andreas Krug
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2012
Extension Groups Of Tautological Sheaves On Hilbert Schemes Of Points On Surfaces written by Andreas Krug and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
In this thesis cohomological invariants of tensor products of tautological objects in the derived category of Hilbert schemes of points on surfaces are studied. The main tool is the Bridgeland-King-Reid-Haiman equivalence between the derived category of the Hilbert scheme and the equivariant derived category of the cartesian power of the surface. The work of Scala on this topic is further developed leading to a new description of the image of tensor products of tautological bundles under the BKRH equivalence. This description leads to formulas for the Euler characteristics of triple tensor products of tautological objects for arbitrary n and for arbitrary tensor products in the case n=2. Furthermore a formula for the extension groups between tautological objects is proven and the Yoneda product is described.
Algebraic Structures And Moduli Spaces
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Author : Jacques Hurtubise and Eyal Markman
language : en
Publisher: American Mathematical Soc.
Release Date :
Algebraic Structures And Moduli Spaces written by Jacques Hurtubise and Eyal Markman 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 with Algebra, Abstract categories.
This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R 4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.
Lectures On Riemann Surfaces Proceedings Of The College On Riemann Surfaces
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Author : Maurizio Cornalba
language : en
Publisher: World Scientific
Release Date : 1989-06-01
Lectures On Riemann Surfaces Proceedings Of The College On Riemann Surfaces written by Maurizio Cornalba and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-06-01 with Mathematics categories.
Hilbert Schemes Of Points And Infinite Dimensional Lie Algebras
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Author : Zhenbo Qin
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-26
Hilbert Schemes Of Points And Infinite Dimensional Lie Algebras written by Zhenbo Qin 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 2018-02-26 with Hilbert schemes categories.
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes of collections of points (zero-dimensional subschemes) in a smooth algebraic surface . Schemes turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of , including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of and the Gromov–Witten correspondence. The last part of the book presents results about quantum cohomology of and related questions. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.
Donaldson Type Invariants For Algebraic Surfaces
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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.
Lectures On K3 Surfaces
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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-26
Lectures On K3 Surfaces written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.
Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.
Punctual Hilbert Schemes
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Author : Anthony Ayers Iarrobino
language : en
Publisher: American Mathematical Soc.
Release Date : 1977
Punctual Hilbert Schemes written by Anthony Ayers Iarrobino 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 1977 with Mathematics categories.
This paper is about the structure of families of open ideals in the ring [italic]R of power series in two variables. The Hilbert scheme Hilb[italic superscript]n [italic]R parametrizing them is stratified into locally closed subschemes [italic]Z[italic subscript]T, whose dimensions we calculate.
Orbifolds In Mathematics And Physics
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Author : Alejandro Adem
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Orbifolds In Mathematics And Physics written by Alejandro Adem 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 2002 with Mathematics categories.
This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the current state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. By presenting the work of a broad range of mathematicians and physicists who use and study orbifolds, it familiarizes readers with the various points of view and types of results the researchers bring to the subject.