A characterization of the U(Omega,m) sets of a hyperelliptic curve as Omega and m vary

Abstract

In this article we consider a certain distinguished set $U(\Omega ,m)\subseteq \{1,2,\dots ,2g+1,\infty \}$ that can be attached to a marked hyperelliptic curve of genus $g$ equipped with a small period matrix $\Omega$ for its polarized Jacobian. We show that as $\Omega$ and the marking $m$ vary, this set ranges over all possibilities prescribed by an argument of Poor.