Irreducibility and stable rationality of the loci of curves of genus at most six with a marked Weierstrass point

Bullock, Evan

doi:10.1090/S0002-9939-2014-11899-5

Irreducibility and stable rationality of the loci of curves of genus at most six with a marked Weierstrass point
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by Evan M. Bullock PDF

Proc. Amer. Math. Soc. 142 (2014), 1121-1132

Abstract:

Given a numerical semigroup $H\subseteq (\mathbf {Z}_{\geq 0},+)$, we consider the locus $\mathcal {M}_{g,1}^H$ of smooth curves of genus $g$ with a marked Weierstrass point of semigroup $H$. We show that for all semigroups $H$ of genus $g\leq 6$ the locus $\mathcal {M}_{g,1}^H$ is irreducible and that for all but possibly two such semigroups it is stably rational.

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