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arxiv: math/0308097 · v1 · submitted 2003-08-11 · 🧮 math.AG · hep-th· math-ph· math.MP

Virasoro constraints for target curves

Andrei Okounkov , Rahul Pandharipande This is my paper
classification 🧮 math.AG hep-thmath-phmath.MP
keywords curvestargetcohomologyconstraintsdescendentsrelativetheoriesvirasoro
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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.

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