Irreducibility and stable rationality of the loci of Weierstrass points   on curves of genus at most six
  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. 
Evan M. Bullock
math.AG