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Flat Rank Two Vector Bundles on Genus Two Curves (Memoirs of the American Mathematical Society)

Algebra

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About the Author Viktoria Heu, Institut de Recherche Mathematique Avancee (IRMA), Strasbourg, France.Frank Loray, Institut de Recherche Mathematique de Rennes (IRMAR), France. Product 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 $2$ case, connections as above are invariant under the hyperelliptic involution: they descend as rank $2$ 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 $(16,6)$-configuration of the Kummer surface. The authors also recover a Poincare 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 $\mathfrak sl_2$-connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.

Product Specifications

Format: paperback
ASIN: 1470435667
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 30 June 2019
Listed Since: 23 March 2019

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Flat Rank Two Vector Bundles on Genus Two Curves (Memoirs of the American Mathematical Society)

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