A reconstruction of Euler data

Abstract

We apply the mirror principle (see Mirror principle, I, Asian J. Math. 1 (1997), pp. 729-763) to reconstruct the Euler data Q = {Qd}d∈ℕ∪{0} associated to a vector bundle V on ℂPn and a multiplicative class b. This gives a direct way to compute the intersection number Kd without referring to any other Euler data linked to Q. Here Kd is the integral of the cohomology class b(Vd) of the induced bundle Vd on a stable map moduli space. A package "EulerData_MP.m" in Maple V that carries out the actual computation is provided in the electronic version math.AG/0003071 of the current paper. For b, the Chern polynomial, the computation of K1 for the bundle V = T*ℂP2, and Kd, d = 1, 2, 3, for the bundles script O signℂP4(l) with 6 ≤ l ≤ 10 are done using the code and are also included.