Points of order two on theta divisors

TL;DR

This paper establishes a bound on the number of points of order two on theta divisors of principally polarized abelian varieties, with applications to counting square roots of line bundles on curves.

Contribution

It provides a new bound on points of order two on theta divisors and applies this to estimate effective square roots on Jacobian curves.

Findings

Bound on points of order two on theta divisors

Application to estimating square roots of line bundles

Enhanced understanding of abelian variety structures

Abstract

We give a bound on the number of points of order two on the theta divisor of a principally polarized abelian variety A. When A is the Jacobian of a curve C the result can be applied in estimating the number of effective square roots of a fixed line bundle on C.