Vanishing thetanulls on curves with involutions
Arnaud Beauville
TL;DR
This paper extends the understanding of vanishing thetanulls from hyperelliptic curves to any curve with an involution, providing new examples of non-hyperelliptic curves with many vanishing thetanulls.
Contribution
It generalizes known results about theta characteristics and vanishing thetanulls to curves with involutions beyond hyperelliptic cases.
Findings
Analogous results hold for s-invariant theta characteristics on any curve with an involution.
Examples of non-hyperelliptic curves with many vanishing thetanulls are constructed.
The configuration of theta characteristics is characterized for these curves.
Abstract
The configuration of theta characteristics and vanishing thetanulls on a hyperelliptic curve is completely understood. We observe in this note that analogous results hold for the s-invariant theta characteristics on any curve C with an involution s . As a consequence we get examples of non hyperelliptic curves with a high number of vanishing thetanulls.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Mathematical Identities · Advanced Algebra and Geometry