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arXiv · 1410.6845

Vector bundles over a real elliptic curve

Indranil Biswas·Florent Schaffhauser
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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 semi-stable 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.

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Indranil Biswas, Florent Schaffhauser. 2016-01-08. Vector bundles over a real elliptic curve. https://doi.org/10.2140/pjm.2016.283.43

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