Deformation of singular fibers of genus two fibrations and small exotic symplectic 4-manifolds

Abstract

We introduce the 2-nodal spherical deformation of certain singular fibers of genus 2 fibrations, and use such deformations to construct various examples of simply connected minimal symplectic 4-manifolds with small topology. More specifically, we construct new exotic minimal symplectic 4-manifolds homeomorphic but not diffeomorphic to CP 2 #6CP 2 , CP 2 #7CP 2 , and 3CP 2 #kCP 2 for k = 16, 17, 18, 19 using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using g-nodal spherical deformations of certain singular fibers of genus g ≥ 3 fibrations.1991 Mathematics Subject Classification. Primary 57R55; Secondary 57R57, 57M05.

Geography of symplectic Lefschetz fibrations and rational blowdowns

“…most of the above referenced articles start with elliptic fibrations). More recently, Akhmedov and Sakallı utilized the classification of singular fibers on certain holomorphic genus-2 Lefschetz fibrations for rational blowdowns [3].…”