Abstract
We study 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 degree zero 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 Gross, Hacking and Keel. 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 degree zero symplectic cohomology defines a family degenerating to a singular surface obtained by gluing together several affine planes.
Citation
James Pascaleff. "On the symplectic cohomology of log Calabi–Yau surfaces." Geom. Topol. 23 (6) 2701 - 2792, 2019. https://doi.org/10.2140/gt.2019.23.2701
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