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Record Nr. |
UNISA996466560403316 |
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Autore |
Zamora Saiz Alfonso |
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Titolo |
Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration / / Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Descrizione fisica |
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1 online resource (xiii, 127 pages) : illustrations |
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Collana |
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SpringerBriefs in Mathematics |
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Disciplina |
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Soggetti |
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Geometry, Algebraic |
Moduli theory |
Invariants |
Geometria algebraica |
Teoria de mòduls |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 2 Preliminaries -- 2.1 Algebraic Varieties and Groups -- 2.1.1 Algebraic Varieties -- 2.1.2 Group Actions -- 2.2 Sheaf Theory and Schemes -- 2.2.1 Sheaves and Cohomology -- 2.2.2 Schemes -- 2.3 Holomorphic Vector Bundles -- 2.3.1 Vector Bundles -- 2.3.2 Line Bundles -- 2.3.3 Divisors -- 3 Geometric Invariant Theory -- 3.1 Quotients and the Notion of Stability -- 3.2 Hilbert-Mumford Criterion -- 3.3 Symplectic Stability -- 3.4 Examples -- 3.5 Maximal Unstability -- 4 Moduli Space of Vector Bundles -- 4.1 GIT Construction of the Moduli Space -- 4.2 Harder-Narasimhan Filtration -- 4.3 Other Constructions of the Moduli Space of Vector Bundles -- 4.3.1 Analytical Construction of the Moduli Space of Vector Bundles -- 4.3.2 Moduli Space of Representations of the Fundamental Group -- 4.4 Moduli Space of Higgs Bundles -- 4.4.1 Hitchin's Construction -- 4.4.2 Higher Rank and Dimensional Higgs Bundles -- 5 Unstability Correspondence -- 5.1 Correspondence for Vector Bundles -- 5.1.1 Main Correspondence: Holomorphic Vector |
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