On the symplectic cohomology of log CalabiYau surfaces
Abstract
This article studies the symplectic cohomology of affine algebraic surfaces that admit a compactification by a normal crossings anticanonical divisor. Using a toroidal structure near the compactification divisor, we describe the complex computing symplectic cohomology, and compute enough differentials to identify a basis for the degreezero part of the symplectic cohomology. This basis is indexed by integral points in a certain integral affine manifold, providing a relationship to the theta functions of GrossHackingKeel. Included is a discussion of wrapped Floer cohomology of Lagrangian submanifolds and a description of the product structure in a special case. We also show that, after enhancing the coefficient ring, the degreezero symplectic cohomology defines a family degenerating to a singular surface obtained by gluing together several affine planes.
 Publication:

arXiv eprints
 Pub Date:
 April 2013
 DOI:
 10.48550/arXiv.1304.5298
 arXiv:
 arXiv:1304.5298
 Bibcode:
 2013arXiv1304.5298P
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Algebraic Geometry;
 Primary 53D40;
 Secondary 53D37;
 14J33
 EPrint:
 61 pages, 8 figures