An Effective Recursion Formula for Computing Intersection Numbers

Mg,n ψ1 1 · · ·ψ dn n . Witten-Kontsevich theorem [9, 4] provides a recursive way to compute all these intersection numbers. However explicit and effective recursion formulae for computing intersection indices are still very rare and very welcome. Our n-point function formula [5] computes intersection indices recursively by decreasing the number of marked points. So it is natural to ask whether there exists a recursion formula which explicitly expresses intersection indices in terms of intersection indices with strictly lower genus. Motivated by Witten’s KdV coefficient equation and our npoint function formula, we find such a recursion formula. Theorem 1.1. Let dj ≥ 0 and ∑n j=1 dj = 3g + n− 3. Then (2g + n− 1)(2g + n− 2)〈 n