Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2021; 58(2): 419-437

Online first article September 22, 2020      Printed March 1, 2021

https://doi.org/10.4134/JKMS.j200093

Copyright © The Korean Mathematical Society.

Symplectic fillings of quotient surface singularities and minimal model program

Hakho Choi, Heesang Park, Dongsoo Shin

Korea Institute for Advanced Study; Korea Institute for Advanced Study; Chungnam National University

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.

Keywords: Minimal model program, quotient surface singularity, rational blow-down, symplectic antiflip, symplectic filling

MSC numbers: 57R40, 57R55, 14B07

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