The moduli space of stable rank 2 parabolic bundles over an elliptic curve with 3 marked points

2020/07/06 by David Boozer, Boozer, David
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2007.02524

Abstract

We explicitly describe the moduli space M^s(X,3) of stable rank 2 parabolic bundles over an elliptic curve X with trivial determinant bundle and 3 marked points. Specifically, we exhibit M^s(X,3) as a blow-up of an embedded elliptic curve in (\mathbbCP¹)³. The moduli space M^s(X,3) can also be interpreted as the SU(2) character variety of the 3-punctured torus. Our description of M^s(X,3) reproduces the known Poincaré polynomial for this space.

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