Compact Moduli Spaces and Vector Bundles
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| Hauptverfasser: | , , , , |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2012
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| Ausgabe: | 1 |
| Schriftenreihe: | Contemporary Mathematics |
| Schlagworte: | |
| ISBN: | 9780821868997, 0821868993 |
| ISSN: | 0271-4132, 1098-3627 |
| Online-Zugang: | Volltext |
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Inhaltsangabe:
- Compact moduli spaces of surfaces of general type -- Rigid curves on <inline-formula content-type="math/mathml"> M ¯ 0 , n \overline {M}_{0,n} </inline-formula> and arithmetic breaks -- Algebraic and combinatorial Brill-Noether theory -- GIT constructions of log canonical models of <inline-formula content-type="math/mathml"> M ¯<!-- ¯ --> g \overline {M}_g </inline-formula> -- The geometry of the ball quotient model of the moduli space of genus four curves -- Two remarks on the Weierstrass flag -- Chern classes of conformal blocks -- Restrictions of stable bundles -- Orthogonal bundles, theta characteristics and symplectic strange duality -- The splitting principle and singularities -- Igusa quartic and Steiner surfaces -- Green’s conjecture for general covers -- Spaces of sections of quadric surface fibrations over curves
- 5. Hecke correspondences and elementary transformations -- 6. Stable bundles and cohomology -- 7. Projective bundles over limits of hyperelliptic curves -- 8. Limits of sections and Néron models of intermediate Jacobians -- 9. Stability and discriminant curves -- 10. Arithmetic applications -- References
- 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, = ₂ -- 5. =0, arbitrary and ℓ=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 -- The splitting principle and singularities -- 1. Introduction -- 2. The Abstract Splitting Principle -- 3. Applications -- References -- Igusa quartic and Steiner surfaces -- 1. Self-morphism of degree 8 -- 2. Proof of Proposition 1 -- 3. Proof of Theorem 2 -- References -- Green's conjecture for general covers -- 1. Introduction -- 2. Koszul cohomology -- 3. Syzygy conjectures for general étale double covers -- 4. Syzygies of sections of Nikulin surfaces -- 5. Green's conjecture for general covers of plane curves -- 6. Green's conjecture for general triple covers of elliptic curves -- 7. Syzygies of double covers of curves of Clifford dimension 3 -- References -- Spaces of sections of quadric surface fibrations over curves -- 1. Introduction -- Acknowledgments -- 2. Quadratic forms, discriminants, and heights -- 3. Reduction to the discriminant for quadric surface fibrations -- 4. Census of quadric fibrations over ℙ
- Intro -- 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 ℙ² -- 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