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OverviewThe 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. Full Product DetailsAuthor: Viktoria Heu , Frank LorayPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.185kg ISBN: 9781470435660ISBN 10: 1470435667 Pages: 107 Publication Date: 30 July 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationViktoria Heu, Institut de Recherche Mathematique Avancee (IRMA), Strasbourg, France. Frank Loray, Institut de Recherche Mathematique de Rennes (IRMAR), France. Tab Content 6Author Website:Countries AvailableAll regions |