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

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

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Author(s):	Viktoria Heu

Date:	2024	Format:	pdf	Language:	English	ISBN/ASIN:	1470435667
Pages:	103	OCR:		Quality:		ISBN13:
Uploader:	risotor	Upload Date:	6/12/2024 9:44:54 AM

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1470435667 pdf
"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" 
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