We study the intersection theory on the moduli spaces of maps of n-pointed curves f : (C, s 1 , . . . , sn) → V which are stable with respect to the weight data (a 1 , . . . , an), 0 a i 1. After describing the structure of these moduli spaces, we prove a formula describing the way descendant invariants change under a wall crossing. As a corollary, we compute the weighted descendants in terms of the usual ones, i.e. for the weight data (1, . . . , 1), and vice versa.
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