| Description |
1 online resource (v, 103 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society ; number 1247 |
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Memoirs of the American Mathematical Society ; no. 1247.
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| Contents |
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 |
| Summary |
"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 case, connections as above are invariant under the hyperelliptic involution: they descend as rank 2 logarithmic connections over the Riemann sphere. We establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows us to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical (16, 6)-configuration of the Kummer surface. We also recover a Poincarape family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. We explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. We explicitly describe the isomonodromic foliation in the moduli space of vector bundles with sl2-connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles"-- Provided by publisher |
| Notes |
Keywords: Vector Bundles, moduli spaces, parabolic connections, Higgs bundles, Kummer surface |
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"May 2019 - Volume 259 - Number 1247 (fourth of 8 numbers)." |
| Bibliography |
Includes bibliographical references |
| Notes |
Print version record |
| Subject |
Vector bundles.
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Moduli theory.
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Differential equations, Parabolic.
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Arithmetical algebraic geometry.
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Ecuaciones diferenciales
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Módulos, Teoría de
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Geometría algebraica aritmética
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Moduli theory
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Differential equations, Parabolic
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Arithmetical algebraic geometry
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Vector bundles
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| Form |
Electronic book
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| Author |
Loray, Frank, 1965-
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| LC no. |
2019023419 |
| ISBN |
1470452499 |
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9781470452490 |
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1470435667 |
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9781470435660 |
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