Volume 23, issue 2 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Floer cohomology, multiplicity and the log canonical threshold

Mark McLean

Geometry & Topology 23 (2019) 957–1056
Abstract

Let f be a polynomial over the complex numbers with an isolated singularity at 0. We show that the multiplicity and the log canonical threshold of f at 0 are invariants of the link of f viewed as a contact submanifold of the sphere.

This is done by first constructing a spectral sequence converging to the fixed-point Floer cohomology of any iterate of the Milnor monodromy map whose E1 page is explicitly described in terms of a log resolution of f. This spectral sequence is a generalization of a formula by A’Campo. By looking at this spectral sequence, we get a purely Floer-theoretic description of the multiplicity and log canonical threshold of f.

Keywords
log canonical threshold, Floer cohomology, singularity, Zariski conjecture, multiplicity, symplectic geometry, contact geometry
Mathematical Subject Classification 2010
Primary: 14J17, 32S55, 53D10, 53D40
References
Publication
Received: 7 March 2018
Revised: 11 August 2018
Accepted: 11 October 2018
Published: 8 April 2019
Proposed: Leonid Polterovich
Seconded: Dan Abramovich, Yasha Eliashberg
Authors
Mark McLean
Department of Mathematics
SUNY Stony Brook
Stony Brook, NY
United States