Abstract

On a stack of stable maps, the cotangent line classes are modified by subtracting certain boundary divisors. These modified cotangent line classes are compatible with forgetful morphisms, and are well-suited to enumerative geometry: tangency conditions allow simple expressions in terms of modified cotangent line classes. Topological recursion relations are established among their top products in genus 0, yielding effective recursions for characteristic numbers of rational curves in any projective homogeneous variety. In higher genus, the obtained numbers are only virtual, due to contributions from spurious components of the space of maps. For the projective plane, the necessary corrections are determined in genus 1 and 2 to give the characteristic numbers in these cases.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 611-647
Launched on MUSE
2002-06-01
Open Access
No
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