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A Lefschetz fibration on minimal symplectic fillings of a quotient surface singularity

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Abstract

In this article, we construct a genus-0 or genus-1 positive allowable Lefschetz fibration on any minimal symplectic filling of the link of non-cyclic quotient surface singularities. As a byproduct, we also show that any minimal symplectic filling of the link of quotient surface singularities can be obtained from a sequence of rational blowdowns from its minimal resolution.

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Acknowledgements

Jongil Park is supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1602-02. He also holds a joint appointment at KIAS and in the Research Institute of Mathematics, SNU.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Korea

    Hakho Choi & Jongil Park

  2. Korea Institute for Advanced Study, Hoegiro 85, Dongdaemun-gu, Seoul, 02455, Korea

    Hakho Choi & Jongil Park

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  1. Hakho Choi
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  2. Jongil Park
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Correspondence to Jongil Park.

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Choi, H., Park, J. A Lefschetz fibration on minimal symplectic fillings of a quotient surface singularity. Math. Z. 295, 1183–1204 (2020). https://doi.org/10.1007/s00209-019-02387-6

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