Cohomological Intersection Numbers for the Generalized Airy Functions at Veronese Points

Abstract

We establish the exterior power structure for the polynomial twisted de Rham cohomology group associated with the generalized Airy functions at a point of extended Veronese variety. Using this structure, we obtain a natural basis of the twisted de Rham cohomology group from that of one dimensional case, which is considered as an analogue of the flat basis of the Jacobi ring of A-type simple singularity. We compute explicitly the cohomological intersection numbers for these basis and extend the result of Iwasaki and Matsumoto.