Circular spherical divisors and their contact topology

Abstract

This paper investigates the symplectic and contact topology associated to circular spherical divisors. We classify, up to toric equivalence, all concave circular spherical divisors $D$ that can be embedded symplectically into a closed symplectic 4-manifold and show they are all realized as symplectic log Calabi-Yau pairs if their complements are minimal. We then determine the Stein fillability and rational homology type of all minimal symplectic fillings for the boundary torus bundles of such $D$. When $D$ is anticanonical and convex, we give explicit betti number bounds for Stein fillings of its boundary contact torus bundle.

40 pages. Fixed typos and improved exposition, as suggested by the referee. To appear in Comm. Anal. Geom