Automorphisms of Curves and Weierstrass semigroups

TL;DR

This paper explores the connection between Weierstrass semigroups and curve invariants, introducing a new filtration for Galois covers and examining their relation to ramification, with applications to invariants like Hasse-Witt.

Contribution

It introduces a novel filtration of the decomposition subgroup for Galois covers and investigates its relation to ramification and invariants of curves.

Findings

New filtration of the group decomposition subgroup for Galois covers

Relation between the filtration and ramification in cyclic covers

Applications to Hasse-Witt invariant and symmetric semigroups

Abstract

The relation of the Weierstrass semigroup with several invariants of a curve is studied. For Galois covers of curves with group $G$ we introduce a new filtration of the group decomposition subgroup of $G$. The relation to the ramification filtration is investigated in the case of cyclic covers. We relate our results to invariants defined by Boseck and we study the one point ramification case. We also give applications to Hasse-Witt invariant and symmetric semigroups.