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＜電子ブック＞
Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration / by Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XIII, 127 p. 16 illus., 12 illus. in color : online resource
著者標目	*Zamora Saiz, Alfonso author Zúñiga-Rojas, Ronald A author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Mathematical physics FREE:Algebraic Geometry FREE:Mathematical Methods in Physics
一般注記	Preface -- Introduction -- Preliminaries -- Geometric Invariant Theory -- Moduli Space of Vector Bundles -- Unstability Correspondence -- Stratifications on the Moduli Space of Higgs Bundles -- References -- Index This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry HTTP:URL=https://doi.org/10.1007/978-3-030-67829-6

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