Abstract
We describe the Stein handlebody diagrams of Milnor fibers of Brieskorn singularities xp +yq +zr = 0. We also study the natural symplectic operation by exchanging two Stein fillings of the canonical contact structure on the links in the case p = q = r, where one of the fillings comes from the minimal resolution and the other is the Milnor fiber. We give two different interpretations of this operation, one as a symplectic sum and the other as a monodromy substitution in a Lefschetz fibration.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1047-1069 |
| Number of pages | 23 |
| Journal | Journal of Symplectic Geometry |
| Volume | 19 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2021 |
Bibliographical note
Funding Information:This project has started on January 2019, while the first author was visiting Harvard University. AA would like to thank the Department of Mathematics at Harvard University for its hospitality. AA was partially supported by a Simons Research Fellowship and Collaboration Grant for Mathematicians from the Simons Foundation. Part of this work was done while C¸ K visited SS at MPIM, and SS visited C¸ K at IMBM. We would like to thank both MPIM and IMBM for their hospitality and support. We are all very grateful to L. Katzarkov for some helpful discussions. We would like to thank Marco Golla for his interest and comments on our work. We are also very grateful to the referee for constructive comments and suggestions that helped to improve the manuscript.
Publisher Copyright:
© 2021, International Press, Inc.. All rights reserved.