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

Séverin Philip

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arXiv · 2608.10742

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

Séverin Philip

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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.

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Séverin Philip. 2026-08-11. Finite monodromy groups in degenerating families and the stability degree of curves. https://arxiv.org/abs/2608.10742

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