Related papers: Virasoro Constraints for Toric Bundles
We prove a conjecture of Artur Elezi in a generalized form suggested by Givental. Namely, our main result relates genus-0 Gromov--Witten invariants of a bundle space with such invariants of the base, provided that the fiber is a toric…
We construct an I-function for toric bundles obtained as a fiberwise GIT quotient of a (not necessarily split) vector bundle. This is a generalization of Brown's I-function for split toric bundles and the I-function for non-split projective…
A conjecture expressing genus 1 Gromov-Witten invariants in mirror-theoretic terms of semi-simple Frobenius structures and complex oscillating integrals is formulated. The proof of the conjecture is given for torus-equivariant Gromov -…
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 Gromov-Witten theory for stable maps with the…
Let E be a toric fibration arising from symplectic reduction of a direct sum of line bundles over (almost-) K\"ahler base B. Then each torus-fixed point of the toric manifold fiber defines a section of the fibration. Let L_a be convex line…
The purpose of this paper is to study Virasoro constraints for Hodge integrals in Gromov-Witten theory of any target varieties. Results consist of the following: Firstly, we propose Virasoro conjecture for Hodge integrals in Gromov-Witten…
In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten theory with many new recent developments in the sheaf theoretic context. In this paper, we rephrase the sheaf-theoretic Virasoro constraints in terms of…
In this paper, we show that the derivative of the genus-1 Virasoro conjecture for Gromov-Witten invariants along the direction of quantum volume element holds for all smooth projective varieties. This result provides new evidence for the…
Virasoro constraints for orbifold Gromov-Witten theory are described. These constraints are applied to the degree zreo, genus zero orbifold Gromov-Witten potentials of the weighted projective stacks $\mathbb{P}(1,N)$, $\mathbb{P}(1,1,N)$…
Given a smooth projective variety $X$ and a smooth nef divisor $D$, we identify genus zero relative Gromov--Witten invariants of $(X,D)$ with $(n+1)$ relative markings with genus zero orbifold Gromov--Witten invariants of multi-root stacks…
Let X be a Gorenstein orbifold and let Y be a crepant resolution of X. We state a conjecture relating the genus-zero Gromov--Witten invariants of X to those of Y, which differs in general from the Crepant Resolution Conjectures of Ruan and…
The Virasoro conjecture is a conjectured sequence of relations among the descendent Gromov-Witten invariants of a smooth projective variety in all genera; the only varieties for which it is known to hold are a point (Kontsevich) and…
We investigate the effect of a general toric wall crossing on genus zero Gromov-Witten theory. Given two complete toric orbifolds $X_+$ and $X_-$ related by wall crossing under variation of GIT, we prove that their respective $I$-functions…
We use techniques from Gromov-Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety. When the matroid is realizable by a complex hyperplane…
We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums…
Brown proved that the I-function of a toric fibration lies on the overruled Lagrangian cone of its genus zero Gromov-Witten theory, introduced by Coates and Givental. In this paper, we prove the theorem for partial flag variety fibrations.…
We use the mirror theorem for toric Deligne-Mumford stacks, proved recently by the authors and by Cheong-Ciocan-Fontanine-Kim, to compute genus-zero Gromov-Witten invariants of a number of toric orbifolds and gerbes. We prove a mirror…
We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.
In this article we propose a definition of super Gromov-Witten invariants by postulating a torus localization property for the odd directions of the moduli spaces of super stable maps and super stable curves of genus zero. That is, we…
The toral rank conjecture speculates that the sum of the Betti numbers of a compact manifold admitting a free action of a torus of rank $r$ is bounded from below by $2^r$. Clearly, such an action yields a torus bundle, and, more generally,…