Explicit constructions of K3 surfaces and unirational Noether–Lefschetz divisors

Abstract

We provide methods to construct explicit examples of K3 surfaces. This leads to unirational constructions of Noether–Lefschetz divisors inside the moduli space of K3 surfaces of genus g. We implement Mukai's unirationality construction of the moduli spaces of K3 surfaces of genus g∈{6,…,10,12}, and we also present a new constructive proof of the unirationality of the moduli space of K3 surfaces of genus 11. Furthermore, we show the existence of three unirational hypersurfaces in any moduli space of K3 surfaces of genus g.