Compact moduli spaces and vector bundles : conference on compact moduli and vector bundles, October 21-24, 2010, University of Georgia, Athens, Georgia / / Valery Alexeev [and four others], editors

• Record Nr.: UNINA9910788636103321
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2012]; ©2012
• ISBN: 0-8218-8537-5
• Descrizione fisica: 1 online resource (264 p.)
• Collana: Contemporary mathematics, ; 564 , 0271-4132
• Classificazione: 14D2214D2014H1014H6014J10
• Disciplina: 514/.224
• Soggetti: Vector bundles; Moduli theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Preface -- Talks at the UGA conference -- Compact moduli spaces of surfaces of general type -- 1. Introduction -- 2. Moduli of stable surfaces -- 3. Infinitesimal study of the moduli stack -- 4. Wahl singularities -- 5. Orbifold double normal crossing singularities -- 6. Surfaces with boundary -- 7. Plane curves -- 8. Exceptional vector bundles associated to degenerations of surfaces -- 9. Boundary divisors of the moduli space of stable surfaces -- 10. Relation with Donaldson theory -- 11. Other examples of boundary divisors -- References -- Rigid curves on \{ }_{0, } and arithmetic breaks -- 1. Introduction -- 2. The Keel-M\textsuperscript{c}Kernan theorem -- 3. Surfaces in \ { }_{0, } from configurations of points in â??² -- 4. The hypergraph construction -- 5. The dual Hesse configuration and a rigid curve on \ { }_{0,12} -- 6. The "Two Conics" construction -- 7. Arithmetic break of a hypergraph curve -- 8. Rigid matroids -- 9. Arithmetic break of a "Two Conics" curve - part I -- 10. Arithmetic break of a "Two Conics" curve - part II -- References -- Algebraic and combinatorial Brill-Noether theory -- 1. Introduction -- 2. Algebro-geometric preliminaries -- 3. Divisor theory on graphs -- 4. Baker specialization lemma refined -- 5. Specialization for graphs with loops -- 6. On the emptyness of Brill-Noether loci -- References -- GIT constructions of log canonical models of \ { }_{ } -- 1. Introduction ; -- 2. Parameter spaces -- 3. Finite Hilbert Stability -- 4. Unstable curves: Degenerate and non-reduced curves -- 5. Unstable curves: Badly singular curves and special subcurves -- 6. Local study of the moduli spaces of c-semistable and of h-semistable curves -- References -- The geometry of the ball quotient model of the moduli space of genus four curves -- Introduction -- 1. Preliminaries on canonical genus 4 curves and cubic 3-folds -- 2. GIT for =4 curves via cubic 3-folds -- 3. Stability for canonical genus 4 curves -- 4. Hassett"Keel Program -- 5. Ball quotient model for the moduli of genus 4 curves -- 6. The comparison of the GIT and ball quotient models -- References -- Two remarks on the Weierstrass flag -- 1. Introduction -- 2. Linear series of Weierstrass type -- 3. On the Weierstrass flags -- References -- Chern classes of conformal blocks -- 1. Introduction -- 2. Conformal blocks -- 3. The case =0 -- 4. =0, = â?? -- 5. =0, arbitrary and â??=1 -- 6. The case >0 -- 7. Questions -- References -- Restrictions of stable bundles -- References -- Orthogonal bundles, theta characteristics and symplectic strange duality -- 1. Introduction -- 2. Moduli spaces -- 3. Hitchin's connection and the geometric Segal-Sugawara tensor -- 4. The proof of Proposition 2.2 -- References.