Virasoro constraints for target curves

2003/08/11 by Andrei Okounkov, Okounkov, Andrei, Rahul Pandharipande +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.AG #math.MP

paper · pdf · doi:10.48550/arxiv.math/0308097

80 pages, 6 figures

arxiv created 2003/08/11 · arxiv updated 2009/12/01

Abstract

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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• The quantum integrable hierarchy for the Gromov-Witten theory of elliptic curves
• Quantization and Algebraic Index

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