KIAS Lectures on Symplectic Aspects of Degenerations

TL;DR

This paper provides an expository account of symplectic aspects of degenerations of complex surfaces, focusing on cyclic quotient surface singularities, based on lectures given at a workshop.

Contribution

It offers a detailed exposition on symplectic aspects of degenerations, particularly for cyclic quotient surface singularities, consolidating lecture notes into a permanent record.

Findings

Clarifies symplectic structures in degenerations of complex surfaces

Provides insights into cyclic quotient surface singularities

Serves as a reference for symplectic aspects in algebraic degenerations

Abstract

This is a series of three lectures I gave at the Korea Institute of Advanced Study in June 2019 at a workshop about "Algebraic and Symplectic Aspects of Degenerations of Complex Surfaces". I focus on the symplectic aspects, in particular on the case of cyclic quotient surface singularities. These notes have been available on a public Git repository since 2019, and I noticed that people occasionally cited them in the years since. For that reason, I decided to post them on arXiv for a more permanent record; I have made some small corrections and annotations but otherwise they are unchanged. These notes are a purely expository account of stuff I was thinking about 2016-2019, and are largely self-aggrandising.