Vol. 283, No. 1, 2016

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Vector bundles over a real elliptic curve

Indranil Biswas and Florent Schaffhauser

Vol. 283 (2016), No. 1, 43–62

Given a geometrically irreducible smooth projective curve of genus 1 defined over the field of real numbers, and a pair of integers r and d, we determine the isomorphism class of the moduli space of semistable vector bundles of rank r and degree d on the curve. When r and d are coprime, we describe the topology of the real locus and give a modular interpretation of its points. We also study, for arbitrary rank and degree, the moduli space of indecomposable vector bundles of rank r and degree d, and determine its isomorphism class as a real algebraic variety.

Elliptic curves, vector bundles on curves, real algebraic varieties
Mathematical Subject Classification 2010
Primary: 14H52, 14H60, 14P25
Received: 21 September 2015
Revised: 28 December 2015
Accepted: 7 January 2016
Published: 14 June 2016
Indranil Biswas
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Mumbai 400005
Florent Schaffhauser
Departamento de Matemáticas
Universidad de Los Andes