Local Complete Intersections and Weierstrass Points

TL;DR

This paper proves that the moduli space of certain Gorenstein curves with specified Weierstrass semigroups is a weighted projective space, extending results to positive characteristic fields when the monomial curve is a local complete intersection.

Contribution

It provides a simple proof connecting local complete intersection properties to the structure of the moduli space in algebraic geometry.

Findings

Moduli space is a weighted projective space for these curves.

The result holds over fields of positive characteristic.

The proof simplifies previous approaches.

Abstract

This work presents a simple proof that the moduli space of complete integral Gorenstein curves with a prescribed symmetric Weierstrass semigroup becomes a weighted projective space, even for fields of positive characteristic, when the associated monomial curve is a local complete intersection.