LEADER 03436nam 2200589 450 001 996466560403316 005 20230421122021.0 010 $a3-030-67829-6 035 $a(CKB)4100000011807163 035 $a(MiAaPQ)EBC6527498 035 $a(Au-PeEL)EBL6527498 035 $a(OCoLC)1243349702 035 $a(PPN)254721311 035 $a(EXLCZ)994100000011807163 100 $a20211014d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration /$fAlfonso Zamora Saiz, Ronald A. Zu?n?iga-Rojas 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (xiii, 127 pages) $cillustrations 225 1 $aSpringerBriefs in Mathematics 311 $a3-030-67828-8 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 2 Preliminaries -- 2.1 Algebraic Varieties and Groups -- 2.1.1 Algebraic Varieties -- 2.1.2 Group Actions -- 2.2 Sheaf Theory and Schemes -- 2.2.1 Sheaves and Cohomology -- 2.2.2 Schemes -- 2.3 Holomorphic Vector Bundles -- 2.3.1 Vector Bundles -- 2.3.2 Line Bundles -- 2.3.3 Divisors -- 3 Geometric Invariant Theory -- 3.1 Quotients and the Notion of Stability -- 3.2 Hilbert-Mumford Criterion -- 3.3 Symplectic Stability -- 3.4 Examples -- 3.5 Maximal Unstability -- 4 Moduli Space of Vector Bundles -- 4.1 GIT Construction of the Moduli Space -- 4.2 Harder-Narasimhan Filtration -- 4.3 Other Constructions of the Moduli Space of Vector Bundles -- 4.3.1 Analytical Construction of the Moduli Space of Vector Bundles -- 4.3.2 Moduli Space of Representations of the Fundamental Group -- 4.4 Moduli Space of Higgs Bundles -- 4.4.1 Hitchin's Construction -- 4.4.2 Higher Rank and Dimensional Higgs Bundles -- 5 Unstability Correspondence -- 5.1 Correspondence for Vector Bundles -- 5.1.1 Main Correspondence: Holomorphic Vector Bundles -- 5.1.2 Other Correspondences for Augmented Bundles -- 5.2 Quiver Representations -- 5.3 (G,h)-Constellations -- 6 Stratifications on the Moduli Space of Higgs Bundles -- 6.1 Shatz Stratification -- 6.2 C-Action and Bia?ynicki-Birula Stratification -- 6.3 Stratifications in Rank Three -- 6.3.1 Sketch of the Proof of Theorem 6.1 -- 6.3.2 Relationship Between Shatz and Bi?ynicki-Birula Stratifications for Rank Three Higgs Bundles -- 6.4 Homotopy Groups -- References -- Index. 410 0$aSpringerBriefs in mathematics. 606 $aGeometry, Algebraic 606 $aModuli theory 606 $aInvariants 606 $aGeometria algebraica$2thub 606 $aTeoria de mòduls$2thub 606 $aInvariants$2thub 608 $aLlibres electrònics$2thub 615 0$aGeometry, Algebraic. 615 0$aModuli theory. 615 0$aInvariants. 615 7$aGeometria algebraica 615 7$aTeoria de mòduls 615 7$aInvariants 676 $a516.35 700 $aZamora Saiz$b Alfonso$0845493 702 $aZu?n?iga-Rojas$b Ronald A. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466560403316 996 $aGeometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration$91891081 997 $aUNISA