Moduli spaces of twisted K3 surfaces and cubic fourfolds

TL;DR

This paper constructs moduli spaces for polarized twisted K3 surfaces of any fixed degree and order, inspired by their relation to special cubic fourfolds, using a quotient of a bounded symmetric domain.

Contribution

It introduces a method to build moduli spaces of twisted K3 surfaces for any fixed degree and order, extending the classical construction for untwisted surfaces.

Findings

Successfully constructed moduli spaces for twisted K3 surfaces.

Extended the classical moduli space construction to twisted cases.

Provided a geometric framework relating twisted K3s and cubic fourfolds.

Abstract

Motivated by the relation between (twisted) K3 surfaces and special cubic fourfolds, we construct moduli spaces of polarized twisted K3 surfaces of any fixed degree and order. We do this by mimicking the construction of the moduli space of untwisted polarized K3 surfaces as a quotient of a bounded symmetric domain.