Abstract
We apply the mirror principle (see Mirror principle, I, Asian J. Math. 1 (1997), pp. 729–763) to reconstruct the Euler data Q = { Q d } d ∈ N ∪ { 0 } Q=\{Q_d\}_{d\in {\mathbb N}\cup \{0\}} associated to a vector bundle V V on C P n {\mathbb C}{\mathrm P}^n and a multiplicative class b b . This gives a direct way to compute the intersection number K d K_d without referring to any other Euler data linked to Q Q . Here K d K_d is the integral of the cohomology class b ( V d ) b(V_d) of the induced bundle V d V_d 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 b , the Chern polynomial, the computation of K 1 K_1 for the bundle V = T ∗ C P 2 V=T_{\ast }{\mathbb C}{\mathrm P}^2 , and K d K_d , d = 1 , 2 , 3 d=1,2,3 , for the bundles O C P 4 ( l ) {\mathcal O}_{{\mathbb C}{\mathrm P}^4}(l) with 6 ≤ l ≤ 10 6\le l\le 10 are done using the code and are also included.