On polarized K3 surfaces of genus 33

TL;DR

This paper proves that the moduli space of smooth primitively polarized K3 surfaces of genus 33 is unirational, contributing to the understanding of their geometric structure.

Contribution

It establishes the unirationality of the moduli space for K3 surfaces of genus 33, a previously unresolved case.

Findings

The moduli space of genus 33 K3 surfaces is unirational.

Provides new insights into the geometry of polarized K3 surfaces.

Advances classification of K3 surfaces by their moduli spaces.

Abstract

We prove that the moduli space of smooth primitively polarized $\mathrm{K3}$ surfaces of genus 33 is unirational.