Finite monodromy groups in degenerating families and the stability degree of curves

Abstract

We compute the stability degree of curves of genus g and show that it is equal to the classical Minkowsky bound. We also compute the stability degree of semi-abelian varieties with prescribed toric and abelian ranks. The proof uses a specialization result for finite monodromy groups in degenerating families, obtained from a variant of Krasner's lemma, together with an explicit construction at the prime 2.

Revised version. Theorem 3.4 and its proof have been clarified. Several typos and notation issues have been corrected. The main results are unchanged