2/22/2007

Michael Usher
Princeton University

Minimality, Kodaira dimension, and symplectic sums

I'll explain how pseudoholomorphic curves can be combined with several other techniques to give simple necessary and sufficient conditions for a symplectic four-manifold arising as a symplectic sum along surfaces of positive genus to be minimal, or to have nonpositive Kodaira dimension. Among other things, this gives a new way of showing that certain small four-manifolds are exotic, and proves a conjecture of Stipsicz about the minimality of fiber sums of Lefschetz fibrations.