Flat Rank Two Vector Bundles on Genus Two Curves

Released on by Viktoria Heu
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  • Flat Rank Two Vector Bundles on Genus Two Curves Book Detail

  • Author : Viktoria Heu
  • Release Date : 2019-06-10
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 116
  • ISBN 13 : 1470435667
  • File Size : 47,47 MB
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Flat Rank Two Vector Bundles on Genus Two Curves by Viktoria Heu PDF Summary

Book Description: The authors 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 they compute a natural Lagrangian rational section. As a particularity of the genus case, connections as above are invariant under the hyperelliptic involution: they descend as rank logarithmic connections over the Riemann sphere. The authors 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 the authors to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical -configuration of the Kummer surface. The authors also recover a Poincaré family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. They 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. They explicitly describe the isomonodromic foliation in the moduli space of vector bundles with -connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.

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Compact Quotients of Cahen-Wallach Spaces

Compact Quotients of Cahen-Wallach Spaces

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Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous fami