A Thomae-like Formula: Algebraic Computations of Theta Constants

Türkü Özlüm Çelik

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Submission date: 25. Jan. 2019
Pages: 25
published in: International mathematics research notices (2019), pp not yet known
DOI number (of the published article): 10.1093/imrn/rnz302
Bibtex
with the following different title: Thomae-Weber formula : algebraic computations of theta constants
MSC-Numbers: 14H42, 14Q05
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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.