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Floer cohomology,
multiplicity and the log canonical threshold
Mark McLean |
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Geometry & Topology 23 (2019) 957–1056
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Abstract |
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Let be a polynomial over the complex numbers with an isolated singularity at . We show that the multiplicity and the log canonical threshold of at are invariants of the link of 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 page is explicitly described in terms of a log resolution of . 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 . |
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Keywords
log canonical threshold, Floer cohomology, singularity,
Zariski conjecture, multiplicity, symplectic geometry,
contact geometry
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Mathematical Subject Classification 2010
Primary: 14J17, 32S55, 53D10, 53D40
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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
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Authors |
| Mark McLean | |
| Department of Mathematics SUNY Stony Brook Stony Brook, NY United States |
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