Irreducibility and stable rationality of the loci of Weierstrass points on curves of genus at most six

TL;DR

This paper proves that for curves of genus up to six, the loci of Weierstrass points with specific semigroups are irreducible and mostly stably rational, advancing understanding of their geometric structure.

Contribution

It establishes irreducibility and stable rationality of Weierstrass point loci for low-genus curves, covering all but two semigroups, which was previously unknown.

Findings

Loci are irreducible for all semigroups of genus ≤ 6

Most loci are stably rational, except possibly two cases

Results apply to curves of genus up to six

Abstract

We show that for any numerical semigroup H of genus g at most 6, the locus of Weierstrass points on curves of genus g with Weierstrass semigroup H is irreducible and that for all but possibly two semigroups it is stably rational.