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Record Nr. |
UNINA9910816105303321 |
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Autore |
Heu Viktoria (1982-) |
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Titolo |
Flat rank two vector bundles on genus two curves / / Viktoria Heu, Frank Loray |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [2019] |
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©2019 |
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ISBN |
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Descrizione fisica |
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1 online resource (v, 103 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; Volume 259, Number 1247 |
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Disciplina |
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Soggetti |
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Fiber bundles (Mathematics) |
Curves, Algebraic |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"Volume 259, number 1247 (fourth of 8 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Sommario/riassunto |
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"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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