Local Gromov-Witten theory of shrinkable surfaces
Abstract: The study of local enumerative invariants of a smooth del Pezzo surface has a long history and is now a well-established subject. Recently from studies on M-theory, local theories for wider classes of algebraic surfaces, known as shrinkable surfaces, are expected. In this talk, I'll present an attempt to generalize the local theory of a smooth del Pezzo surface to a shrinkable surface using the Gromov-Witten theory. In particular, I'll describe how to define the local Gromov-Witten invariants for some del Pezzo surfaces with normal crossing singularities. This is joint work with Sheldon Katz.