KSB smoothings of surface pairs

TL;DR

This paper explores KSB smoothings of log canonical surface pairs with reduced curves, revealing that cyclic quotient pairs always admit such smoothings and often have multiple irreducible components.

Contribution

It introduces the concept of KSB smoothings for surface pairs with reduced divisors, highlighting differences from the case without divisors and providing new existence results.

Findings

Cyclic quotient pairs always have KSB smoothings.

KSB smoothings can form many irreducible components.

Contrast with the case where D is empty.

Abstract

We describe KSB smoothings of log canonical surface pairs $(S, D)$, where $D$ is a reduced curve. In sharp contrast with the $D=\emptyset$ case, cyclic quotient pairs always have KSB smoothings, usually forming many irreducible components. v.2: References added, small changes.