书目名称 | Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration | 编辑 | Alfonso Zamora Saiz,Ronald A. Zúñiga-Rojas | 视频video | | 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 | 丛书名称 | SpringerBriefs in Mathematics | 图书封面 |  | 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 | 关键词 | algebraic geometry; geometric invariant theory; GIT; Harder-Narasimham filtration; vector bundles; Higgs | 版次 | 1 | doi | https://doi.org/10.1007/978-3-030-67829-6 | isbn_softcover | 978-3-030-67828-9 | isbn_ebook | 978-3-030-67829-6Series ISSN 2191-8198 Series E-ISSN 2191-8201 | issn_series | 2191-8198 | copyright | The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 |
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