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

DOI: 10.2140/pjm.2020.304.1

Abstract

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.

Keywords

real vector bundle, hyperelliptic curve, moduli space

Mathematical Subject Classification 2010

Primary: 14D20, 14P05

Milestones

Received: 29 October 2018

Revised: 22 February 2019

Accepted: 22 July 2019

Published: 18 January 2020