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The moduli space of
real vector bundles of rank two over a real hyperelliptic
curve
Thomas John Baird and Shengda Hu |
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Vol. 304 (2020), No. 1, 1–14
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Abstract |
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The Desale–Ramanan theorem is an isomorphism between the moduli space of rank two vector bundles over complex hyperelliptic curve and the variety of linear subspaces in an intersection of two quadrics. We prove a real version of this theorem for the moduli space of real vector bundles over a real hyperelliptic curve. We then apply this result to study the topology of the moduli space, proving that it is relatively spin and identifying the diffeomorphism type for genus two curves. Our results lay the groundwork for future study of the quantum homology of these moduli spaces. |
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Keywords
real vector bundle, hyperelliptic curve, moduli space
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Mathematical Subject Classification 2010
Primary: 14D20, 14P05
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Milestones
Received: 29 October 2018
Revised: 22 February 2019
Accepted: 22 July 2019
Published: 18 January 2020
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Authors |
| Thomas John Baird | |
| Department of Mathematics &
Statistics Memorial University of Newfoundland St. John’s NL Canada |
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| Shengda Hu | |
| Department of Mathematics Wilfrid Laurier University Waterloo ON Canada |
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