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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 |
| Sumario: | "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"-- |
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| Notas: | Keywords: Vector Bundles, moduli spaces, parabolic connections, Higgs bundles, Kummer surface "May 2019 - Volume 259 - Number 1247 (fourth of 8 numbers)." |
| Descripción Física: | 1 online resource (v, 103 pages) : illustrations |
| Bibliografía: | Includes bibliographical references. |
| ISBN: | 1470452499 9781470452490 1470435667 9781470435660 |