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Moduli of weighted stable maps and their gravitational descendants

Valery Alexeev·G. Michael Guy
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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.

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Valery Alexeev, G. Michael Guy. 2007-11-13. Moduli of weighted stable maps and their gravitational descendants. https://arxiv.org/abs/math/0607683

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