#### 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
##### Abstract

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.

##### Keywords
Elliptic curves, vector bundles on curves, real algebraic varieties
##### Mathematical Subject Classification 2010
Primary: 14H52, 14H60, 14P25