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Flat rank two vector bundles on genus two curves /
"We study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which we compute a natural Lagrangian rational section. As a particularity of the genus 2...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
[2019]
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1247. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Chapter 1. Preliminaries on connections; 1.1. Logarithmic connections; 1.2. Twists and trace; 1.3. Projective connections and Riccati foliations; 1.4. Parabolic structures; 1.5. Elementary transformations; 1.6. Stability and moduli spaces; Chapter 2. Hyperelliptic correspondence; 2.1. Topological considerations; 2.2. A direct algebraic approach; Chapter 3. Flat vector bundles over; 3.1. Flatness criterion; 3.2. Semi-stable bundles and the Narasimhan-Ramanan theorem; 3.3. Semi-stable decomposable bundles; 3.4. Semi-stable indecomposable bundles
- 3.5. Unstable and indecomposable: the 6+10 Gunning bundles3.6. Computation of a system of coordinates; Chapter 4. Anticanonical subbundles; 4.1. Tyurin subbundles; 4.2. Extensions of the canonical bundle; 4.3. Tyurin parametrization; Chapter 5. Flat parabolic vector bundles over the quotient /; 5.1. Flatness criterion; 5.2. Dictionary: how special bundles on occur as special bundles on /; 5.3. Semi-stable bundles and projective charts; 5.4. Moving weights and wall-crossing phenomena; 5.5. Galois and Geiser involutions; 5.6. Summary: the moduli stack \BUN( )
- Chapter 6. The moduli stack ℌ ( ) and the Hitchin fibration6.1. A Poincaré family on the 2-fold cover \HIGGS( / ); 6.2. The Hitchin fibration; 6.3. Explicit Hitchin Hamiltonians on \HIGGS( / ); 6.4. Explicit Hitchin Hamiltonians on \HIGGS( ); 6.5. Comparison to existing formulae; Chapter 7. The moduli stack ℭ ( ); 7.1. An explicit atlas; 7.2. The apparent map on \CON( / ); 7.3. A Lagrangian section of \CON( )→\BUN( ); Chapter 8. Application to isomonodromic deformations; 8.1. Darboux coordinates; 8.2. Hamiltonian system; 8.3. Transversality to the locus of Gunning bundles
- 8.4. Projective structures and Hejhal's theorem