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[null,"1.","Record Nr.",null,"UNINA9910483216103321"]
[null,null,"Autore",null,"Zamora Saiz Alfonso"]
[null,null,"Titolo",null,"Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration / / Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas"]
[null,null,"Pubbl/distr/stampa",null,"Cham, Switzerland : , : Springer, , [2021]"]
[{"$nulls":4},"©2021"]
[null,null,"ISBN",null,"3-030-67829-6"]
[null,null,"Descrizione fisica",null,"1 online resource (xiii, 127 pages) : illustrations"]
[null,null,"Collana",null,"SpringerBriefs in Mathematics"]
[null,null,"Disciplina",null,"516.35"]
[null,null,"Soggetti",null,"Geometry, Algebraic"]
[{"$nulls":4},"Moduli theory"]
[{"$nulls":4},"Invariants"]
[{"$nulls":4},"Geometria algebraica"]
[{"$nulls":4},"Teoria de mòduls"]
[{"$nulls":4},"Llibres electrònics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"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 "]
[{"$nulls":4},"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."]