Meromorphic Matrix Trivializations of Factors of Automorphy over a Riemann Surface

Joseph A. Ball; Kevin F. Clancey; Victor Vinnikov

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arXiv · 1510.07931

Meromorphic Matrix Trivializations of Factors of Automorphy over a Riemann Surface

Joseph A. Ball·Kevin F. Clancey·Victor Vinnikov

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Abstract

It is a consequence of the Jacobi Inversion Theorem that a line bundle over a Riemann surface M of genus g has a meromorphic section having at most g poles, or equivalently, the divisor class of a divisor D over M contains a divisor having at most g poles (counting multiplicities). We explore various analogues of these ideas for vector bundles and associated matrix divisors over M. The most explicit results are for the genus 1 case. We also review and improve earlier results concerning the construction of automorphic or relatively automorphic meromorphic matrix functions having a prescribed null/pole structure.

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Joseph A. Ball, Kevin F. Clancey, Victor Vinnikov. 2015-10-27. Meromorphic Matrix Trivializations of Factors of Automorphy over a Riemann Surface. https://arxiv.org/abs/1510.07931

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