Variety of Singular Quadrics Containing a Projective Curve

Abstract

We study the variety of rank $\le k$ quadrics containing a general projective curve and show that it has the expected dimension in the range $g-d+r\le 1$. By considering the loci where this expectation is not true, we construct new divisor classes in ${\overline{\mathcal{M}}}_{g,n}$. We use one of these classes to show that ${\overline{\mathcal{M}}}_{15,9}$ is of general type.

References in corpus (2)

• Quadric rank loci on moduli of curves and K3 surfaces
• Maximal Rank Divisors on ${\overline{\mathcal{M}}}_{g,n}$