Flat rank two vector bundles on genus two curves
Viktoria Heu
Bok · Engelsk · 2019
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| Omfang | v, 103 sider : figurer
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| Opplysninger | "May 2019, volume 259, number 1247 (fourth of 8 numbers)" - Tittelbladet. - På omslaget: MEMO/259/1247. - "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 Langrangian 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 Poincaré family due to Bolognesi on a degree 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" - Referat, side v
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| ISBN | 978-1-4704-3566-0
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