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arXiv · 2607.06494

Classification of equivariantly normal curves via Altmann-Hausen-S\"uss theory

Gary Martínez-Núnez·Ronan Terpereau
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Abstract

Let the ground field be perfect of positive characteristic. Using Altmann-Hausen-S\"uss theory, we obtain a combinatorial classification of equivariantly normal curves with prescribed quotient in both the affine and projective settings. As a consequence, we derive an explicit upper bound on the number of isomorphism classes of equivariantly normal curves over a fixed base curve with prescribed branch locus. Furthermore, assuming that the ground field is algebraically closed, we determine, for a fixed cardinality of the branch locus, precisely when the set of isomorphism classes of equivariantly normal projective curves with prescribed quotient is finite and when it is infinite.

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Gary Martínez-Núnez, Ronan Terpereau. 2026-07-07. Classification of equivariantly normal curves via Altmann-Hausen-S\"uss theory. https://arxiv.org/abs/2607.06494

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