Type II Degenerations of K3 Surfaces of Degree 4

TL;DR

This paper investigates Type II degenerations of degree 4 K3 surfaces, constructing explicit Tyurin degenerations for boundary components of their moduli space and analyzing their stable models.

Contribution

It provides explicit constructions of Tyurin degenerations for all boundary components of the moduli space of degree 4 K3 surfaces.

Findings

Constructed explicit Tyurin degenerations for each boundary component.

Developed 18-dimensional families of degenerations.

Computed stable models of these degenerations.

Abstract

We study Type II degenerations of K3 surfaces of degree 4 where the central fiber consists of two rational components glued along an elliptic curve. Such degenerations are called Tyurin degenerations. We construct explicit Tyurin degenerations corresponding to each of the 1-dimensional boundary components of the Baily-Borel compactification of the moduli space of K3 surfaces of degree 4. For every such boundary component we also construct an 18-dimensional family of Tyurin degenerations of K3 surfaces of degree 4 and compute the stable models of these degenerations.