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      A Thomae-like Formula: Algebraic Computations of Theta Constants

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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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          Most cited references 8

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          The Magma Algebra System I: The User Language

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            On the equations defining abelian varieties. I

             D. Mumford (1966)
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              Theorie der Abel'schen Functionen.

               B. Riemann (1857)
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                Author and article information

                Journal
                24 January 2019
                Article
                1901.08459

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                14H42, 14Q05
                23 pages, no figures
                math.AG

                Geometry & Topology

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