LEADER 02830nam 2200469 450 001 9910816105303321 005 20190812132802.0 010 $a1-4704-5249-9 035 $a(CKB)4100000008483126 035 $a(MiAaPQ)EBC5788253 035 $a(PPN)23729088X 035 $a(EXLCZ)994100000008483126 100 $a20190627d2019 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFlat rank two vector bundles on genus two curves /$fViktoria Heu, Frank Loray 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2019] 210 4$dİ2019 215 $a1 online resource (v, 103 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 259, Number 1247 300 $a"Volume 259, number 1247 (fourth of 8 numbers)." 311 $a1-4704-3566-7 320 $aIncludes bibliographical references. 330 $a"We study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which we compute a natural Lagrangian rational section. As a particularity of the genus 2 case, connections as above are invariant under the hyperelliptic involution: they descend as rank 2 logarithmic connections over the Riemann sphere. We establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows us to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical (16, 6)-configuration of the Kummer surface. We also recover a Poincarape family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. We explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. We explicitly describe the isomonodromic foliation in the moduli space of vector bundles with sl2-connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 259, Number 1247. 606 $aFiber bundles (Mathematics) 606 $aCurves, Algebraic 615 0$aFiber bundles (Mathematics) 615 0$aCurves, Algebraic. 676 $a514.224 700 $aHeu$b Viktoria$f(1982-),$01722437 702 $aLoray$b Frank 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816105303321 996 $aFlat rank two vector bundles on genus two curves$94122783 997 $aUNINA