Moduli of weighted stable maps and their gravitational descendants

Details Moduli of weighted stable maps and their gravitational descendants Moduli of weighted stable maps and their gravitational descendants

2006-07-26

arxiv.org/abs/math/0607683v4

Mathematics

Algebraic Geometry

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

Scientific paper

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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