version math.AG/0311208 THE CLOSED TOPOLOGICAL VERTEX VIA THE CREMONA TRANSFORM

ABSTRACT. We compute the local Gromov-Witten invariants of the “closed vertex”, that is, a configuration of three ’s meeting in a single triple point in a Calabi-Yau threefold. The method is to express the local invariants of the vertex in terms of ordinary Gromov-Witten invariants of a certain blowup of and then to compute those invariants via the geometry of the Cremona transformation. 1