# Seminar in Algebraic Geometry and Number Theory

Jan Stevens, Chalmers/GU: Pointed curves with prescribed Weierstrass semigroup

Abstract: On a smooth projective curve each point has a Weierstrass gap sequence, and the non-gaps form a numerical semigroup. The space parametrising smooth pointed curves with given Weierstrass semigroup at the marked point is a locally closed subspace of the moduli space of pointed curves.

We provide a new lower bound for the dimension of this space. It is based on the connection with the deformation theory of the monomial curve with the same semigroup. For certain families of curves this space is computed explicitly, showing that the lower bound is attained, and that the corresponding moduli spaces are non-empty and of pure dimension.

Organisers: Anders Södergren (andesod@chalmers.se) and Christian Johansson (chrjohv@chalmers.se). Please contact one of us if you wish to be informed of future seminars.

This is a hybrid seminar. Join via Zoom: https://chalmers.zoom.us/j/67079766743

Page manager Published: Fri 14 Jan 2022.