相关论文: Gromov--Witten theory of $[\mathbb{C}^2/\mathbb{Z}…
We compute open GW invariants for $\mathcal{K}_{\mathbb{P}^1}\oplus\mathcal{O}_{\mathbb{P}^1}$, open orbifold GW invariants for $[\C^3/\Z_2]$, formulate an open crepant resolution conjecture and verify it for this pair. We show that open…
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)…
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…
We use Pixton's relations to prove a reconstruction theorem for genus 2 Gromov-Witten invariants in the style of Kontsevich-Manin (genus 0) and Getzler (genus 1). We also calculate genus 2 (descendant) Gromov-Witten invariants of…
Let $\mathcal{X}_1$ and $\mathcal{X}_2$ be smooth proper Deligne-Mumford stacks with projective coarse moduli spaces. We prove a formula for orbifold Gromov-Witten invariants of the product stack $\mathcal{X}_1\times \mathcal{X}_2$ in terms…
Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X and an invertible multiplicative characteristic class. Special cases…
For any finite abelian group G, the equivariant Gromov-Witten invariants of C^r/G can be viewed as a certain kind of abelian Hurwitz-Hodge integrals. In this note, we use Tseng's orbifold quantum Riemann-Roch theorem to express this kind of…
For any finite group $G$, the equivariant Gromov-Witten invariants of $[\mathbb{C}^r/G]$ can be viewed as a certain twisted Gromov-Witten invariants of the classifying stack $\mathcal{B} G$. In this paper, we use Tseng's orbifold quantum…
We study the orbifold Gromov-Witten theory of the quotient C^3/Z_3 in all genera. Our first result is a proof of the holomorphic anomaly equations in the precise form predicted by B-model physics. Our second result is an exact crepant…
We study the Abramovich--Vistoli moduli space of genus zero orbifold stable maps to [Sym^2 P^2], the stack symmetric square of P^2. This compactifies the moduli space of stable maps from hyperelliptic curves to P^2, and we show that all…
We calculate the genus 1 Gromov-Witten theory of the Hilbert scheme $\mathsf{Hilb}^n(\mathbb{C}^2)$ of points in the plane. The fundamental 1-point invariant (with a divisor insertion) is calculated using a correspondence with the families…
The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed…
We study the relationship between Gromov-Witten invariants of local $\mathbb{P}^4$ and Gromov-witten invariants of $[\mathbb{C}^5/\mathbb{Z}_5]$ for all genera. We state the crepant resolution conjecture in explicit form and prove this…
We derive a formula for the virtual class of the moduli space of rubber maps to $[\mathbb{P}^1/G]$ pushed forward to the moduli space of stable maps to $BG$. As an application, we show that the Gromov-Witten theory of $[\mathbb{P}^1/G]$…
The study of open/closed string duality and large $N$ duality suggests a Gromov-Witten theory for conifolds that sits on the border of both a closed Gromov-Witten theory and an open Gromov-Witten theory. In this work we employ the result of…
We define equivariant open Gromov-Witten invariants for $\mathbb{R}\mathbb{P}^{2m} \hookrightarrow \mathbb{C}\mathbb{P}^{2m}$ as sums of integrals of equivariant forms over resolution spaces, which are blowups of products of moduli spaces…
For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the Gromov-Witten theories of the orbifold and the resolution. We prove the conjecture for the…
This is the sequel to the author's previous paper which gives an extension of Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds. The main result of this paper asserts the following. Whenever the Seiberg-Witten invariants are defined…
We explore the theory of connected Gromov-Witten invariants of the symmetric product stack [Sym^n(A_r)]. We derive closed-form expressions for all equivariant invariants with two insertions and reveal a natural correspondence between the…
We study the relative orbifold Donaldson-Thomas theory of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$. We establish a correspondence between the DT theory relative to 3 fibers to quantum multiplication by divisors in the Hilbert…