# GW/PT Descendent Correspondence via Vertex Operators

@article{Oblomkov2018GWPTDC, title={GW/PT Descendent Correspondence via Vertex Operators}, author={Alexei Oblomkov and Andrei Okounkov and Rahul Pandharipande}, journal={Communications in Mathematical Physics}, year={2018}, volume={374}, pages={1321-1359} }

We propose an explicit formula for the $${{\mathsf {GW}}}/{\mathsf {PT}}$$ GW / PT descendent correspondence in the stationary case for nonsingular connected projective threefolds. The formula, written in terms of vertex operators, is found by studying the 1-leg geometry. We prove the proposal for all nonsingular projective toric threefolds. An application to the Virasoro constraints for the stationary descendent theory of stable pairs will appear in a sequel.

#### 9 Citations

EGL formula for DT/PT theory of local curves

- Mathematics, Physics
- 2019

In this note we prove an integral formula for the bare one-leg PT vertex with descendents.
The formula follows from the PT version of Ellingsrud-Gottsche-Lehn formula that is explained here. We… Expand

Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of $\mathbb{P}[r]$

- Physics, Mathematics
- 2019

We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line $\mathbb P[r]$. Furthermore, we deduce the explicit bilinear… Expand

Virasoro constraints for stable pairs on toric 3-folds

- Mathematics
- 2020

Using new explicit formulas for the stationary GW/PT descendent correspondence for nonsingular projective toric 3-folds, we show that the correspondence intertwines the Virasoro constraints in… Expand

QUANTUM CURVE AND BILINEAR FERMIONIC FORM FOR THE ORBIFOLD GROMOV-WITTEN THEORY OF P[r]

- 2019

We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line P[r]. Furthermore, we deduce the explicit bilinear Fermionic… Expand

Double nested Hilbert schemes and the local stable pairs theory of curves

- Mathematics, Physics
- 2021

We propose a variation of the classical Hilbert scheme of points — the double nested Hilbert scheme of points — which parametrizes flags of zero-dimensional subschemes whose nesting is dictated by a… Expand

Virasoro conjecture for the stable pairs descendent theory of simply connected 3-folds (with applications to the Hilbert scheme of points of a surface)

- Mathematics
- 2020

This paper concerns the recent Virasoro conjecture for the theory of stable pairs on a 3-fold proposed by Oblomkov, Okounkov, Pandharipande and the author in arXiv:2008.12514. Here we extend the… Expand

Virasoro constraints in quantum singularity theories

- Mathematics, Physics
- 2021

We introduce Virasoro operators for any Landau-Ginzburg pair (W,G) where W is a non-degenerate quasi-homogeneous polynomial and G is a certain group of diagonal symmetries. We propose a conjecture… Expand

Moduli spaces of semistable pairs on projective Deligne-Mumford stacks

- Mathematics
- 2020

We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a… Expand

Rationality of descendent series for Hilbert and Quot schemes of surfaces

- Mathematics
- 2020

Quot schemes of quotients of a trivial bundle of arbitrary rank on a nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf… Expand

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