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arXiv · 1901.08459

A Thomae-like Formula: Algebraic Computations of Theta Constants

Turku Ozlum Celik
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Abstract

We give an algebraic method to compute the fourth power of the quotient of any even theta constants associated to a given non-hyperelliptic curve in terms of geometry of the curve. In order to apply the method, we work out non-hyperelliptic curves of genus 4, in particular, such curves lying on a singular quadric, which arise from del Pezzo surfaces of degree 1. Indeed, we obtain a complete 2-level structure of the curves by studying their theta characteristic divisors via exceptional divisors of the del Pezzo surfaces as the structure is required for the method.

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Turku Ozlum Celik. 2019-01-24. A Thomae-like Formula: Algebraic Computations of Theta Constants. https://arxiv.org/abs/1901.08459

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