A vanishing result for tautological classes on the moduli of K3 surfaces

TL;DR

This paper proves a vanishing theorem for the tautological cohomology ring of the moduli space of K3 surfaces, analogous to Looijenga's theorem for curves, revealing new structural insights.

Contribution

It establishes a vanishing result for tautological classes on the moduli space of K3 surfaces, extending known results from curves to K3 surfaces.

Findings

Tautological cohomology ring vanishes above a certain degree for K3 moduli.

Analogous vanishing theorem to Looijenga's for K3 surfaces.

Provides new structural understanding of K3 moduli space.

Abstract

Looijenga's vanishing theorem on the moduli space of curves $M_g$ says that the tautological ring vanishes above degree $g-2$. We prove an analogous result for the tautological cohomology ring of the moduli space of K3 surfaces.