On wormholes in the moduli space of surfaces

TL;DR

This paper investigates a wormholing phenomenon in the moduli space of surfaces of general type, caused by extremal P-resolutions, and proves a general conjecture for many cases.

Contribution

It introduces a general wormhole conjecture in the KSBA compactification and proves it for a broad class of cases, advancing understanding of the moduli space topology.

Findings

Wormholing occurs due to extremal P-resolutions in the KSBA boundary

The paper proves the wormhole conjecture in many cases

Discussion of topological properties and open questions

Abstract

We study a certain wormholing phenomenon that takes place in the Koll\'ar--Shepherd-Barron--Alexeev (KSBA) compactification of the moduli space of surfaces of general type. It occurs because of the appearance of particular extremal P-resolutions in surfaces on the KSBA boundary. We state a general wormhole conjecture, and we prove it for a wide range of cases. At the end, we discuss some topological properties and open questions.