03436nam 2200589 450 99646656040331620230421122021.03-030-67829-6(CKB)4100000011807163(MiAaPQ)EBC6527498(Au-PeEL)EBL6527498(OCoLC)1243349702(PPN)254721311(EXLCZ)99410000001180716320211014d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGeometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration /Alfonso Zamora Saiz, Ronald A. Zúñiga-RojasCham, Switzerland :Springer,[2021]©20211 online resource (xiii, 127 pages) illustrationsSpringerBriefs in Mathematics3-030-67828-8 Includes bibliographical references and index.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.SpringerBriefs in mathematics.Geometry, AlgebraicModuli theoryInvariantsGeometria algebraicathubTeoria de mòdulsthubInvariantsthubLlibres electrònicsthubGeometry, Algebraic.Moduli theory.Invariants.Geometria algebraicaTeoria de mòdulsInvariants516.35Zamora Saiz Alfonso845493Zúñiga-Rojas Ronald A.MiAaPQMiAaPQMiAaPQBOOK996466560403316Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration1891081UNISA