Vol. 304, No. 1, 2020

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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

Vol. 304 (2020), No. 1, 1–14

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.

real vector bundle, hyperelliptic curve, moduli space
Mathematical Subject Classification 2010
Primary: 14D20, 14P05
Received: 29 October 2018
Revised: 22 February 2019
Accepted: 22 July 2019
Published: 18 January 2020
Thomas John Baird
Department of Mathematics & Statistics
Memorial University of Newfoundland
St. John’s NL
Shengda Hu
Department of Mathematics
Wilfrid Laurier University
Waterloo ON