Gromov-Witten theory, Hurwitz theory, and completed cycles
By A. Okounkov, R. Pandharipande. 2002
452 citations recorded by the source corpus.
We establish an explicit equivalence between the stationary sector of the Gromov-Witten theory of a target curve X and the enumeration of Hurwitz coverings of X in the basis of completed cycles. The stationary sector is formed, by definition, by the descendents of the point class. Completed cycles arise naturally in the theory of shifted symmetric functions. Using this equivalence, we give a complete description of the stationary Gromov-Witten theory of the projective line and elliptic curve. Toda equations for the relative stationary theory of the projective line are derived.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/cd737b30a9fa26c10607d2807571dc7be9b0961b
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In Algebra and Number Theory
- Nick Scott
- Paul T. Norbury
- A. Okounkov
- R. Pandharipande
- A. Eskin
- Dimitri Zvonkine
- Sergey Shadrin
- L. Spitz
In Geometry and Topology
- R. Pandharipande
- Marcos Mariño
- Nick Scott
- Paul T. Norbury
- A. Okounkov
- V. Bouchard
- Boris Dubrovin
- Dimitri Zvonkine
Citations in the corpus
- The Extended Toda Hierarchy (2003, result): “Probably, one can derive our Toda conjecture from the results of Okounkov and Pandharipande [24, 25] using the arguments of Getzler’s paper [15] along with the Givental’s result.”
- Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, background): “Theorem 2.4 (Okounkov, Pandharipande [31]).”
- Virasoro constraints for target curves (2003, methodology): “We first review the formula for the descendents of ω obtained from the GW/H correspondence and the theory of completed cycles [ 11 ].”
- The Equivariant Gromov-Witten theory of P**1 (2002, methodology): “In the first paper [22], we considered the stationary sector of the Gromov-Witten theory of X formed by the descendents of ω.”
- Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants (2011, methodology): “The Gromov-Witten invariants of P1 have been studied and well understood over the last ten years [11, 14, 15, 16].”