Virasoro constraints for target curves

By A. Okounkov, R. Pandharipande. 2003

165 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6b0022dbbdb50f991f2375c1ac1cbb3bd3b37400

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Integrals of ψ-classes over double ramification cycles (2012, background): “of Theorem 1, namely, the case when as = 0 while all other ai’s do not vanish. The case where as = 0 and some other ai’s may also vanish is covered by a more general computation in Proposition 2.5 of [12]. Actually, we don’t have an independent proof for the case as = 0 we just invoke the above resu”
Gromov-Witten/pairs correspondence for the quintic 3-fold (2012, methodology): “11) of [27], by studying the descendents”
Curves on K3 surfaces and modular forms (2010, background): “For the general case, we need only to check that quasi-modularity is preserved by the extended Virasoro relations for curves proved in [42] which provide rules for removing the insertions τk(γ) for γ ∈ H (1)(E,Z).”
The local Donaldson–Thomas theory of curves (2005, methodology): “The technique, following Gromov–Witten theory (see Maulik–Pandharipande [26] and Okounkov–Pandharipande [30]), involves rigidification and topological recursion.”
Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants (2011, methodology): “The Virasoro constraints enable one to calculate non-stationary invariants from stationary invariants but does not determine the stationary invariants [16].”
Relative virtual localization and vanishing of tautological classes on moduli spaces of curves (2003, background): “s of some of the results of Section 5), and [LLZ1, LLZ2]. Relative virtual localization also plays an essential role in Okounkov and Pandharipande’s proof of the Virasoro constraints for target curve [OPa]. Throughout this paper we work over C, or any other algebraically closed ﬁeld of characteristi”
A mathematical theory of the topological vertex (2004, methodology): “We introduce moduli spaces of relative stable maps to the non-rigid (P(1), {0,∞}) (called rubber in [41] etc.”
A topological view of Gromov-Witten theory (2004, background): “denote the moduli space of stable maps to Y relative to both divisors, and let M •∼ =M •∼ g,n(Y/D0 ∪D∞, β, → μ, → ν ) denote the corresponding space of stable maps to a non-rigid target — termed a rubber target in [4, 19].”