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Titlebook: Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration; Alfonso Zamora Saiz,Ronald A. Zú?iga-Rojas Bo

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發(fā)表于 2025-3-21 18:11:25 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
編輯Alfonso Zamora Saiz,Ronald A. Zú?iga-Rojas
視頻videohttp://file.papertrans.cn/384/383529/383529.mp4
概述Introduces key topics on Geometric Invariant Theory through examples and applications.Covers Hilbert classification of binary forms and Hitchin‘s theory on Higgs bundles.Takes particular note of unsta
叢書(shū)名稱SpringerBriefs in Mathematics
圖書(shū)封面Titlebook: Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration;  Alfonso Zamora Saiz,Ronald A. Zú?iga-Rojas Bo
描述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 geo
出版日期Book 2021
關(guān)鍵詞algebraic geometry; geometric invariant theory; GIT; Harder-Narasimham filtration; vector bundles; Higgs
版次1
doihttps://doi.org/10.1007/978-3-030-67829-6
isbn_softcover978-3-030-67828-9
isbn_ebook978-3-030-67829-6Series ISSN 2191-8198 Series E-ISSN 2191-8201
issn_series 2191-8198
copyrightThe Author(s), under exclusive license to Springer Nature Switzerland AG 2021
The information of publication is updating

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發(fā)表于 2025-3-21 20:35:37 | 只看該作者
Book 2021an 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 geo
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Drugs for Neurological Disorders,nclude a brief summary of sheaves, cohomology, and schemes, because those are the objects with which to develop this theory in full generality. Finally, essentials about holomorphic vector bundles, line bundles, and divisors are discussed.
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Stratifications on the Moduli Space of Higgs Bundles, rank. We thus analyze the relation between the two stratifications for the moduli space of rank three Higgs bundles, based on results contained in [., .,.,.]. This relation allows some applications, as the computation of homotopy groups of the moduli space.
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Unstability Correspondence, explained, say holomorphic pairs, Higgs bundles, and rank 2 tensors. Moreover, a similar correspondence is performed in a different setting, the moduli space of quiver representations on vector spaces which generalizes to an infinite-dimensional setting in the moduli problem of constellations yielding an asymptotic correspondence.
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