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Tangency quantum cohomology

Published online by Cambridge University Press:  04 December 2007

Joachim Kock
Joachim Kock
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco, Cidade Universitária 50670-901, Recife, PE, [email protected]
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Abstract

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Let X be a smooth projective variety. Using modified psi classes on the stack of genus-zero stable maps to X, a new associative quantum product is constructed on the cohomology space of X. When X is a homogeneous variety, this structure encodes the characteristic numbers of rational curves in X, and specialises to the usual quantum product upon resetting the parameters corresponding to the modified psi classes. For $X=\mathbb{P}^2$, the product is equivalent to that of the contact cohomology of Ernström and Kennedy.

Keywords

quantum cohomologyGromov–Witten invariantsenumerative geometry14N35 (primary)53D45 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 1 , January 2004 , pp. 165 - 178
Copyright
Foundation Compositio Mathematica 2004