Geometry of the moduli space of $n$-pointed K3 surfaces of genus 11

Abstract

We prove that the moduli space of polarized $K3$ surfaces of genus eleven with $n$ marked points is unirational when $n\le 6$ and uniruled when $n\le 7$. As a consequence, we settle a long standing but not proved assertion about the unirationality of ${\mathcal{M}}_{11,n}$ for $n\le 6$. We also prove that the moduli space of polarized $K3$ surfaces of genus eleven with $9$ marked points has non-negative Kodaira dimension.

Final version, typos corrected and some proofs simplified. To appear in Bull. London Math. Soc

References in corpus (2)

• Projective Degenerations of K3 Surfaces, Gaussian Maps, and Fano Threefolds
• The Kodaira dimension of the moduli of K3 surfaces