Moduli spaces and vector bundles - new trends

• Titel: Moduli spaces and vector bundles - new trends
• Titelzusatz: VBAC 2022 conference "Moduli spaces and vector bundles - new trends" in honor of Peter Newstead's 80th birthday : July 25-29, 2022, University of Warwick, Coventry, United Kingdom
• Mitwirkende: Gothen, Peter Beier [HerausgeberIn]
• Mitwirkende: Melo, Margarida [HerausgeberIn]
• Mitwirkende: Teixidor i Bigas, Montserrat [HerausgeberIn]
• Gefeierte Person: Newstead, Peter E. [GefeierteR]
• Körperschaft: VBAC 2022 Conference Moduli Spaces and Vector Bundles, New Trends : In honor of Peter Newstead’s 80th Birthday <2022, Coventry> [VerfasserIn]
• Verf.angabe: Peter Gothen, Margarida Melo, Montserrat Teixidor i Bigas (editors)
• Verlagsort: Providence, Rhode Island
• Verlag: American Mathematical Society
• E-Jahr: 2024
• Jahr: [2024]
• Umfang: 1 Online-Ressource (viii, 370 Seiten)
• Gesamttitel/Reihe: Contemporary mathematics ; 803
• Fussnoten: Description based on publisher supplied metadata and other sources
• ISBN: 978-1-4704-7646-5
• Datenträger: Online-Ressource
• Dokumenttyp: Konferenzschrift: (2022 : Coventry)
• Dokumenttyp: Festschrift
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Moduli spaces and vector bundles. - Providence, Rhode Island : American Mathematical Society, 2024. - pages cm
• Sach-SW: Algebraic geometry -- Curves -- Vector bundles on curves and their moduli
• Sach-SW: Algebraic geometry -- Algebraic groups -- Geometric invariant theory
• Sach-SW: Algebraic geometry -- Families, fibrations -- Algebraic moduli problems, moduli of vector bundles
• Sach-SW: Algebraic geometry -- Surfaces and higher-dimensional varieties -- Vector bundles on surfaces and higher-dimensional varieties, and their moduli
• Sach-SW: Algebraic geometry -- Algebraic groups -- Group actions on varieties or schemes (quotients)
• Sach-SW: Differential geometry -- Symplectic geometry, contact geometry -- Symplectic structures of moduli spaces
• Sach-SW: Global analysis, analysis on manifolds -- Spaces and manifolds of mappings -- Moduli problems for topological structures
• Sach-SW: Algebraic geometry -- (Co)homology theory -- Topological properties
• K10plus-PPN: 189753020X
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

This volume contains the proceedings of the VBAC 2022 Conference on Moduli Spaces and Vector Bundles--New Trends, held in honor of Peter Newstead's 80th birthday, from July 25-29, 2022, at the University of Warwick, Coventry, United Kingdom. The papers focus on the theory of stability conditions in derived categories, non-reductive geometric invariant theory, Brill-Noether theory, and Higgs bundles and character varieties. The volume includes both survey and original research articles. Most articles contain substantial background and will be helpful to both novices and experts.

Abstract

Cover -- Title page -- Contents -- Preface -- Poincaré and Picard bundles on the moduli spaces of bundles on curves -- 1. Introduction -- 2. The case of rank 1 -- 3. Poincaré and Picard bundles on Higher Rank Moduli spaces -- 4. Parabolic vector bundles -- References -- Topology of the moduli spaces of Higgs bundles over abelian varieties -- 1. Introduction -- 2. Preliminaries on Character Varieties and Higgs Bundles -- 3. Normality of the Moduli Spaces -- 4. Mixed Hodge Polynomials -- 5. Symplectic singularities and resolutions -- 6. Topology of Resolutions via Hilbert Schemes -- References -- Global properties of Higgs bundle moduli spaces -- 1. Introduction -- 2. The real forms -- 3. -Higgs bundles -- 4. Component types and labels -- 5. Morse-theoretic approach -- 6. Sections of Hitchin fibrations and Hitchin components -- 7. Maximal components and the Cayley correspondence -- 8. Magical triples and generalized Cayley maps -- 9. Remaining cases and loose ends -- 10. Beyond ₀ -- 11. Supplemental Notes -- 12. Tables -- References -- Moduli of unstable bundles of HN-length two with fixed algebra of endomorphisms -- 1. Introduction -- 2. Unstable bundles of HN-lenght 2 -- 3. Algebra of endomorphisms -- 4. Moduli spaces -- 5. Non-emptiness of _{ ₁}( , , ) -- References -- The Brill-Noether Theory of the moduli spaces of sheaves on surfaces -- 1. Introduction -- 2. Preliminaries -- 3. Brill-Noether for curves -- 4. Pathologies for surfaces -- 5. Weak Brill-Noether -- 6. Applications and generalizations of weak Brill-Noether -- 7. Cohomology jumping loci -- References -- Double covers of curves on Nikulin surfaces -- 1. Introduction -- 2. Prym-Brill-Noether theory -- 3. Theta-characteristics and vanishing thetanulls -- 4. Brill-Noether theory for double covers -- 5. Double covers of curves on Nikulin surfaces -- References.