Vertex Algebra And Generalized Complex Geometry

We construct a N = 2 superconformal vertex algebra(SCVA) from a generalizedCalabi-Yau manifold, generalized Ka¨hler maifold and compute the BRST cohomologyof its associated topological vertex algebras. We show that the BRST cohomology co-incided with the generalized Dobeault cohomology. We show that the two topologicalvertex algebras constructed from the N = 2 SCVA by A and B twist respectively aremirror pairs.