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

We introduce the 2-nodal spherical deformation of certain singular fibers of genus two 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.