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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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Pubblicazione: | Cham, Switzerland : , : Springer, , [2021] |
©2021 | |
Descrizione fisica: | 1 online resource (xiii, 127 pages) : illustrations |
Disciplina: | 516.35 |
Soggetto topico: | Geometry, Algebraic |
Moduli theory | |
Invariants | |
Geometria algebraica | |
Teoria de mòduls | |
Soggetto genere / forma: | Llibres electrònics |
Persona (resp. second.): | Zúñiga-RojasRonald A. |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | 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 Bundles -- 5.1.2 Other Correspondences for Augmented Bundles -- 5.2 Quiver Representations -- 5.3 (G,h)-Constellations -- 6 Stratifications on the Moduli Space of Higgs Bundles -- 6.1 Shatz Stratification -- 6.2 C-Action and Białynicki-Birula Stratification -- 6.3 Stratifications in Rank Three -- 6.3.1 Sketch of the Proof of Theorem 6.1 -- 6.3.2 Relationship Between Shatz and Biłynicki-Birula Stratifications for Rank Three Higgs Bundles -- 6.4 Homotopy Groups -- References -- Index. |
Titolo autorizzato: | Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration ![]() |
ISBN: | 3-030-67829-6 |
Formato: | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 996466560403316 |
Lo trovi qui: | Univ. di Salerno |
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