On nonnegatively graded Weierstrass points
Journal article, 2024

We provide a new lower bound for the dimension of the moduli space of smooth pointed curves with prescribed Weierstrass semigroup at the marked point, derived from the Deligne–Greuel formula and Pinkham’s equivariant deformation theory. Using Buchweitz’s description of the first cohomology module of the cotangent complex for monomial curves, we show that our lower bound improves a recently one given by Pflueger. By allowing semigroups running over suitable families of symmetric semigroups of multiplicity six, we show that this new lower bound is attained, and that the corresponding moduli spaces are non-empty and of pure dimension.

moduli of curves

Weierstrass points

equivariant deformation theory

Author

André Contiero

Universidade Federal de Minas Gerais

Aislan Leal Fontes

Federal University of Sergipe

Jan Stevens

Chalmers, Mathematical Sciences

Jhon Quispe Vargas

Federal University of Goiás

Arkiv for Matematik

0004-2080 (ISSN) 18712487 (eISSN)

Vol. 62 2 387-412

Subject Categories

Algebra and Logic

Mathematical Analysis

DOI

10.4310/ARKIV.2024.v62.n2.a4

More information

Latest update

12/11/2024