Descendant invariants and characteristic numbers
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1.
Harvard University
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2.
Royal Institute of Technology
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3.
California Institute of Technology
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.
Copyright and License
© 2002 Johns Hopkins University Press.
Acknowledgement
Part of this work was carried out while the second author was visiting the California Institute of Technology to which he is thankful for exquisite hospitality.
Funding
Research of the first author supported in part by a Sloan dissertation year fellowship and an NSF postdoctoral fellowship; research of the second author supported in part by the Natural Science Research Council of Denmark and the Nordic Research Academy (NorFA).
Additional details
Related works
- Is new version of
- Discussion Paper: https://arxiv.org/abs/math/0102017 (URL)
Funding
- Alfred P. Sloan Foundation
- National Science Foundation
- Danmarks Frie Forskningsfond
- NordForsk
Dates
- Submitted
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2001-06-04
Caltech Custom Metadata
- Caltech groups
- Division of Physics, Mathematics and Astronomy (PMA)
- Publication Status
- Published