THE MODULI SPACE OF STABLE RANK 2 PARABOLIC BUNDLES OVER AN ELLIPTIC CURVE WITH 3 MARKED POINTS

David Boozer

doi:10.1090/proc/15996

THE MODULI SPACE OF STABLE RANK 2 PARABOLIC BUNDLES OVER AN ELLIPTIC CURVE WITH 3 MARKED POINTS

David Boozer

Mathematics

Research output: Contribution to journal › Article › peer-review

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 (CP¹)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.

Original language	English (US)
Pages (from-to)	4645-4653
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	11
DOIs	https://doi.org/10.1090/proc/15996
State	Published - Nov 1 2022

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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abstract = "We explicitly describe the moduli space Ms(X,3) of stable rank 2 parabolic bundles over an elliptic curve X with trivial determinant bundle and 3 marked points. Specifically, we exhibit Ms(X,3) as a blow-up of an embedded elliptic curve in (CP1)3. The moduli space Ms(X,3) can also be interpreted as the SU(2) character variety of the 3-punctured torus. Our description of Ms(X,3) reproduces the known Poincar{\'e} polynomial for this space.",

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N2 - We explicitly describe the moduli space Ms(X,3) of stable rank 2 parabolic bundles over an elliptic curve X with trivial determinant bundle and 3 marked points. Specifically, we exhibit Ms(X,3) as a blow-up of an embedded elliptic curve in (CP1)3. The moduli space Ms(X,3) can also be interpreted as the SU(2) character variety of the 3-punctured torus. Our description of Ms(X,3) reproduces the known Poincaré polynomial for this space.

AB - We explicitly describe the moduli space Ms(X,3) of stable rank 2 parabolic bundles over an elliptic curve X with trivial determinant bundle and 3 marked points. Specifically, we exhibit Ms(X,3) as a blow-up of an embedded elliptic curve in (CP1)3. The moduli space Ms(X,3) can also be interpreted as the SU(2) character variety of the 3-punctured torus. Our description of Ms(X,3) reproduces the known Poincaré polynomial for this space.

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THE MODULI SPACE OF STABLE RANK 2 PARABOLIC BUNDLES OVER AN ELLIPTIC CURVE WITH 3 MARKED POINTS

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