Compact moduli for certain Kodaira fibrations

TL;DR

This paper explicitly describes degenerations of certain Kodaira fibrations within the moduli space of stable surfaces and demonstrates the connectedness of a component of this space under specific conditions.

Contribution

It provides an explicit description of degenerations and establishes connectedness of a moduli space component for a class of Kodaira fibrations.

Findings

Explicit description of degenerations in the moduli space

Connected component of the moduli space identified

Conditions under which the component is connected

Abstract

We describe explicitly the possible degenerations of a class of double Kodaira fibrations in the moduli space of stable surfaces. Using deformation theory we also show that under some assumptions we get a connected component of the moduli space of stable surfaces.