Virasoro constraints for target curves

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.

80 pages, 6 figures

References in corpus (5)

• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• Quantum Cohomology and Virasoro Algebra
• Hodge integrals and degenerate contributions
• The equivariant Gromov-Witten theory of P^1
• Gromov-Witten theory, Hurwitz theory, and completed cycles

Cited by in corpus (6)

• Matrix Models for Random Partitions
• Nonlinear PDEs for Fredholm determinants arising from string equations
• Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
• A short proof of the lambda_g-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
• Symmetric Group Gauge Theories and Simple Gauge/String Dualities
• Les Houches lecture notes on moduli spaces of Riemann surfaces