Virasoro constraints for target curves

A. Okounkov, R. Pandharipande

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


We prove generalized Virasoro constraints for the relative Gromov-Witten theories of all nonsingular target curves. Descendents of the even cohomology classes are studied first by localization, degeneration, and completed cycle methods. Descendents of the odd cohomology are then controlled by monodromy and geometric vanishing relations. As an outcome of our results, the relative theories of target curves are completely and explicitly determined.

Original languageEnglish
Pages (from-to)47-108
Number of pages62
JournalInventiones Mathematicae
Issue number1
Publication statusPublished - Jan 2006
Externally publishedYes


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