Moduli of weighted stable maps and their gravitational descendants

Abstract

We study the intersection theory on the moduli spaces of maps of $n$-pointed curves $f:(C,s_1,...s_n)\to V$ which are stable with respect to a weight data $(a_1,...,a_n)$, $0\le a_i\le 1$. After describing the structure of these moduli spaces, we prove a formula describing the way each descendant changes 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.

v3: mostly typographical edits; v4: minor update following referee's comments

References in corpus (2)

• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
• Tame stacks in positive characteristic