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

Boozer, David

doi:10.1090/proc/15996

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

Proc. Amer. Math. Soc. 150 (2022), 4645-4653

DOI: https://doi.org/10.1090/proc/15996

Published electronically: August 12, 2022

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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 $(\mathbb {CP}^1)^3$. 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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