Maximal Rank Divisors on ${\overline{\mathcal{M}}}_{g,n}$

Abstract

We compute the class of the effective divisors on ${\overline{\mathcal{M}}}_{g,n}$, which are set theoretically equal to the locus of moduli points $[C,p_1,\dots ,p_n]$ where $C$ lies on a quadric under the map given by the linear series $|K_C-p_1-\cdots -p_n|$. Using this divisor class we show that the moduli spaces ${\overline{\mathcal{M}}}_{16,8}$ and ${\overline{\mathcal{M}}}_{17,8}$ are of general type. We also note that the divisor classes computed in the papers \cite{FV1} and \cite{FV2} can be used to show that ${\overline{\mathcal{M}}}_{12,10}$ is of general type as well.

References in corpus (1)

• Limit linear series and ranks of multiplication maps

Cited by in corpus (1)

• Variety of Singular Quadrics Containing a Projective Curve