QUANTUM COHOMOLOGY OF BLOWUPS OF SURFACES AND ITS FUNCTORIALITY PROPERTY*

In this article, using the WDVV equation, the author first proves that all Gromov-Witten invariants of blowups of surfaces can be computed from the Gromov-Witten invariants of itself by some recursive relations. Furthermore, it may determine the quantum product on blowups. It also proves that there is some degree of functoriality of the big quantum cohomology for a blowup.