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


Author: Evan M. Bullock
Journal: Proc. Amer. Math. Soc. 142 (2014), 1121-1132
MSC (2010): Primary 14H45, 14H55; Secondary 14M20, 14E08, 14H10
DOI: https://doi.org/10.1090/S0002-9939-2014-11899-5
Published electronically: January 21, 2014
MathSciNet review: 3162235
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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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Additional Information

Evan M. Bullock
Email: evanmb@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-11899-5
Received by editor(s): June 29, 2011
Received by editor(s) in revised form: April 24, 2012, and May 8, 2012
Published electronically: January 21, 2014
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 Evan M. Bullock