Leung, Naichung Conan; Symington, Margaret Almost toric symplectic four-manifolds. (English) Zbl 1197.53103 J. Symplectic Geom. 8, No. 2, 143-187 (2010). Summary: Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that include both toric manifolds and the K3 surface. We classify closed almost toric four-manifolds up to diffeomorphism and indicate precisely the structure of all almost toric fibrations of closed symplectic four-manifolds. A key step in the proof is a geometric classification of the singular integral affine structures that can occur on the base of an almost toric fibration of a closed four-manifold. As a byproduct we provide a geometric explanation for why a generic Lagrangian fibration over the two-sphere must have 24 singular fibers. Cited in 26 Documents MSC: 53D05 Symplectic manifolds (general theory) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies Keywords:K3 surfaces; closed symplectic four-manifolds; Lagrangian fibration; two-sphere PDF BibTeX XML Cite \textit{N. C. Leung} and \textit{M. Symington}, J. Symplectic Geom. 8, No. 2, 143--187 (2010; Zbl 1197.53103) Full Text: DOI arXiv Euclid OpenURL