Flat rank 2 vector bundles on genus 2 curves
Flat rank 2 vector bundles on genus 2 curves
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属 2 曲线上的平秩 2 向量束
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发表时间：
2014
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通讯作者：
F. Loray
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作者：
Viktoria Heu;F. Loray
本文研究亏格为2的曲线上无迹不可约秩为2的联络的模空间和到其下向量丛（包括不稳定丛）模空间的遗忘映射，并计算了其自然Lagrange有理截面.作为亏格2情形的特殊性，上述联络在超椭圆对合下是不变的：它们在黎曼球面上以秩2对数联络下降。我们建立明确的联系之间的著名的模空间的基础抛物丛与经典的方法Narasimhan-Ramanan，Tyurin和Bertram。这使我们能够解释一定数量的几何现象，在所考虑的模空间，如经典的（16，6）-配置的库默表面。我们还恢复了Poincare家庭由于Bolognesi的度2覆盖的Narasimhan-Ramanan模空间。我们明确计算希格斯包模空间上的希钦可积系统，并与vanGeemen-Previato的希钦哈密顿量进行比较。本文明确地描述了亏格为2的曲线上sl（2，C）-联络向量丛模空间中的等单道叶理，并证明了诱导流与不稳定丛轨迹的横截性。
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 under- lying 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 allow 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 Poincare 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 vanGeemen-Previato. We explicitly describe the isomonodromic foliation in the moduli space of vector bundles with sl(2,C)-connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.