02830nam 2200469 450 991081610530332120190812132802.01-4704-5249-9(CKB)4100000008483126(MiAaPQ)EBC5788253(PPN)23729088X(EXLCZ)99410000000848312620190627d2019 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierFlat rank two vector bundles on genus two curves /Viktoria Heu, Frank LorayProvidence, Rhode Island :American Mathematical Society,[2019]©20191 online resource (v, 103 pages)Memoirs of the American Mathematical Society ;Volume 259, Number 1247"Volume 259, number 1247 (fourth of 8 numbers)."1-4704-3566-7 Includes bibliographical references."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"--Provided by publisher.Memoirs of the American Mathematical Society ;Volume 259, Number 1247.Fiber bundles (Mathematics)Curves, AlgebraicFiber bundles (Mathematics)Curves, Algebraic.514.224Heu Viktoria(1982-),1722437Loray FrankMiAaPQMiAaPQMiAaPQBOOK9910816105303321Flat rank two vector bundles on genus two curves4122783UNINA