A Thomae-like Formula: Algebraic Computations of Theta Constants
Türkü Özlüm Çelik
Contact the author: Please use for correspondence this email.
Submission date: 25. Jan. 2019
MSC-Numbers: 14H42, 14Q05
Download full preprint: PDF (616 kB)
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.