Symplectic fillings of quotient surface singularities and minimal model program

TL;DR

This paper introduces an explicit algorithm, inspired by the minimal model program, to construct all minimal symplectic fillings of quotient surface singularities from their minimal resolutions using rational blow-downs and symplectic antiflips.

Contribution

It provides a novel, algorithmic approach connecting symplectic topology with algebraic geometry techniques for surface singularities.

Findings

All minimal symplectic fillings can be obtained via rational blow-downs and antiflips.

The algorithm is explicit and inspired by the minimal model program.

The method bridges symplectic topology and algebraic geometry for surface singularities.

Abstract

We prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit algorithm inspired by the minimal model program for complex 3-dimensional algebraic varieties.