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weighted stable curves

Journal of the Institute of Mathematics of Jussieu (1)

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MODULI OF WEIGHTED STABLE MAPS AND THEIR GRAVITATIONAL DESCENDANTS
Valery Alexeev, G. Michael Guy
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 7 / Issue 3 / July 2008

Published online by Cambridge University Press:

10 December 2007, pp. 425-456

Print publication:

July 2008
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We study the intersection theory on the moduli spaces of maps of $n$-pointed curves $f:(C,s_1,\dots,s_n)\to V$ which are stable with respect to the weight data $(a_1,\dots,a_n)$, $0\le a_i\le1$. 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 $(1,\dots,1)$, and vice versa.