A note on the Petri loci

Details A note on the Petri loci A note on the Petri loci

2010-12-03

arxiv.org/abs/1012.0856v3

Mathematics

Algebraic Geometry

Final version, to appear on Manuscripta Mathematica

Scientific paper

Let $\M_g$ be the course moduli space of complex projective nonsingular
curves of genus $g$. We prove that when the Brill-Noether number $\rho(g,r,n)$
is non-negative every component of the Petri locus $P^r_{g,n}\subset \M_g$
whose general member is a curve $C$ such that $W^{r+1}_n(C) = \emptyset$, has
codimension one in $\M_g$.

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