Related papers: Genus-1 Virasoro conjecture along quantum volume d…
In our previous work, we provided an algebraic proof of the Zinger's comparison formula between genus one Gromov-Witten invariants and reduced invariants when the target space is a complete intersection of dimension two or three in a…
In their fundamental work, B. Dubrovin and Y. Zhang, generalizing the Virasoro equations for the genus 0 Gromov-Witten invariants, proved the Virasoro equations for a descendent potential in genus 0 of an arbitrary conformal Frobenius…
New relations among the genus-zero Gromov-Witten invariants of a complex projective manifold $X$ are exhibited. When the cohomology of $X$ is generated by divisor classes and classes ``with vanishing one-point invariants,'' the relations…
An effective algorithm of determining Gromov--Witten invariants of smooth hypersurfaces in any genus (subject to a degree bound) from Gromov--Witten invariants of the ambient space is proposed. The Appendix is joint with E. Schulte-Geers.
We prove genus $g$ invariants in quantum $K$-theory are determined by genus zero invariants of a smooth stack in the spirit of K.~Costello's result in Gromov--Witten theory.
We determine the all-genus Hodge-Gromov-Witten theory of a smooth hypersurface in weighted projective space defined by a chain or loop polynomial. In particular, we obtain the first genus-zero computation of Gromov-Witten invariants for…
We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special…
In this paper, we propose a definition of genus one real Gromov-Witten invariants for certain symplectic manifolds with real a structure, including Calabi-Yau threefolds, and use equivariant localization to calculate certain genus one real…
We define Gromov-Witten classes and invariants of smooth projective schemes of finite presentation over a Dedekind domain. We prove that they are deformation invariants and verify the fundamental axioms. For a smooth projective scheme over…
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 study genus 1 Gromov-Witten invariants of Fano complete intersections in the projective spaces. Among other things, we show a reconstruction theorem for genus 1 invariants with only ambient insertions, and compute the genus 1 invariants…
We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds CP^1 and CP^2 (or more generally, smooth projective curves and smooth…
A projected Gromov-Witten variety is the union of all rational curves of fixed degree that meet two opposite Schubert varieties in a homogeneous space X = G/P. When X is cominuscule we prove that the map from a related Gromov-Witten variety…
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 $\mathbb{P}(1,N)$, $\mathbb{P}(1,1,N)$…
We propose two conjectural relationships between the equivariant Gromov-Witten invariants of the resolved conifold under diagonal and anti-diagonal actions and the Gromov-Witten invariants of $\mathbb{P}^1$, and verify their validity in…
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…
We propose an extension of the recently-proposed volume conjecture for closed hyperbolic 3-manifolds, to all orders in perturbative expansion. We first derive formulas for the perturbative expansion of the partition function of complex…
We build the abstract theory of Gromov-Witten invariants of genus 0 for quantum minimal Fano varieties (a minimal natural (with respect to Gromov-Witten theory) class of varieties). In particular, we consider ``the minimal Gromov-Witten…
The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on their properties that are essential for actually working…
Gromov-Witten invariants for arbitrary projective varieties and arbitrary genus are constructed using the techniques from K. Behrend, B. Fantechi: The intrinsic normal cone.