Related papers: Double and Triple Givental's J-functions for Stabl…
The moduli space of stable quotients introduced by Marian-Oprea-Pandharipande provides a natural compactification of the space of morphisms from nonsingular curves to a nonsingular projective variety and carries a natural virtual class. We…
In the first part of this paper, we obtain mirror formulas for twisted genus 0 two-point Gromov-Witten (GW) invariants of projective spaces and for the genus 0 two-point GW-invariants of Fano and Calabi-Yau complete intersections. This…
In this paper we compute certain two-point integrals over a moduli space of stable maps into projective space. Computation of one-point analogues of these integrals constitutes a proof of mirror symmetry for genus-zero one-point…
In this paper, we study the all genus Gromov-Witten theory for any GKM orbifold $X$. We generalize the Givental formula which is studied in the smooth case in \cite{Giv2} \cite{Giv3} \cite{Giv4} to the orbifold case. Specifically, we…
We propose localization techniques for computing Gromov-Witten invariants of maps from Riemann surfaces with boundaries into a Calabi-Yau, with the boundaries mapped to a Lagrangian submanifold. The computations can be expressed in terms of…
We make precise conjectures relating the genus zero Gromov-Witten theory of a nonabelian GIT quotient X//G to that of the associated abelian quotient X//T by a maximal torus T in G.These conjectures imply in particular closed formulas for…
Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…
We show that the standard generating functions for genus 0 two-point twisted Gromov-Witten invariants arising from concavex vector bundles over symplectic toric manifolds are explicit transforms of the corresponding one-point generating…
In this paper we compute genus 0 orbifold Gromov--Witten invariants of Calabi--Yau threefold complete intersections in weighted projective stacks, regardless of convexity conditions. The traditional quantumn Lefschetz principle may fail…
We derive a closed formula for the generating function of genus two Gromov-Witten invariants of quintic 3-folds and verify the corresponding mirror symmetry conjecture of Bershadsky, Cecotti, Ooguri and Vafa.
We give a graph-sum algorithm that expresses any genus-$g$ Gromov-Witten invariant of the symmetric product orbifold $\mathrm{Sym}^d\mathbb{P}^r:=[(\mathbb{P}^r)^d/S_d]$ in terms of "Hurwitz-Hodge integrals" -- integrals over (compactified)…
In algebraic geometry, Gromov--Witten invariants are enumerative invariants that count the number of complex curves in a smooth projective variety satisfying some incidence conditions. In 2001, A. Givental and Y.P. Lee defined new…
We study the enumerative geometry of stable maps to Calabi-Yau 5-folds $Z$ with a group action preserving the Calabi-Yau form. In the central case $Z=X \times \mathbb{C}^2$, where $X$ is a Calabi-Yau 3-fold with a group action scaling the…
In this paper, we exhibit a formula relating punctured Gromov-Witten invariants used by Gross and Siebert to 2-point relative/logarithmic Gromov-Witten invariants with one point-constraint for any smooth log Calabi-Yau pair $(W,D)$. Denote…
The J-function in Gromov-Witten theory is a generating function for one-point genus zero Gromov-Witten invariants with descendants. Here we give formulas for the quantum K-theoretic J-functions of type A flag manifolds and conjectural…
We use the Gromov-Witten/Pairs descendent correspondence for toric 3-folds and degeneration arguments to establish the GW/P correspondence for several compact Calabi-Yau 3-folds (including all CY complete intersections in products of…
Given a smooth projective variety $X$ with a smooth nef divisor $D$ and a positive integer $r$, we construct an $I$-function, an explicit slice of Givental's Lagrangian cone, for Gromov--Witten theory of the root stack $X_{D,r}$. As an…
We obtain mirror formulas for the genus 1 Gromov-Witten invariants of projective Calabi-Yau complete intersections. We follow the approach previously used for projective hypersurfaces by extending the scope of its algebraic results; there…
Givental's $K$-theoretical $J$-function can be used to reconstruct genus zero $K$-theoretical Gromov--Witten invariants. We view this function as a fundamental solution of a $q$-difference system. In the case of projective spaces, we show…
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 -…