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In this article we consider a certain distinguished set $U(\Omega,m)\subseteq \{1,2,\ldots,2g+1,\infty\}$ that can be attached to a markedhyperelliptic 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.

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