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MODULI OF WEIGHTED STABLE MAPS AND THEIR GRAVITATIONAL DESCENDANTS

Published online by Cambridge University Press:  10 December 2007

Valery Alexeev  and
G. Michael Guy
Valery Alexeev
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA (valery@math.uga.edu; guy@math.uga.edu)
G. Michael Guy
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA (valery@math.uga.edu; guy@math.uga.edu)
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Abstract

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.

Keywords

Gromov–Witten invariantsweighted stable mapsgravitational descendantsweighted stable curvesPrimary 14N35Secondary 14D20
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 7 , Issue 3 , July 2008 , pp. 425 - 456
Copyright
2007 Cambridge University Press

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