相关论文: A formula for the total permutation-equivariant K-…

We describe the structure of mirror formulas for genus 0 Gromov-Witten invariants of projective complete intersections with any number of marked points and provide an explicit algorithm for obtaining the relevant structure coefficients. The…

The enumerative geometry of r-th roots of line bundles is the subject of Witten's conjecture and occurs in the calculation of Gromov-Witten invariants of orbifolds. It requires the definition of the suitable compact moduli stack and the…

We introduce a new definition of weighted Grassmann orbifolds. We study their several invariant $q$-cell structures and the orbifold singularities on these $q$-cells. We discuss when the integral cohomology of a weighted Grassmann orbifold…

In this paper, we establish an analog of Dijkgraaf-Witten's theorem for $g=1$ invariants in permutation-equivariant quantum K-theory. This result generalizes the findings of \cite{Tang1} and \cite{Tang2}.

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…

In this paper, we give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying new relations in the tautological ring of the moduli space of 2-pointed…

Let $(X,E)$ be a smooth log Calabi-Yau pair consisting of a smooth Fano surface $X$ and a smooth anticanonical divisor $E$. We obtain certain higher genus local Gromov-Witten invariants from the projectivization of the canonical bundle $Z…

The elliptic quasimap potential function is explicitly calculated for Calabi-Yau complete intersections in projective spaces by Kim and Lho. We extend this result to local Calabi-Yau varieties. Using this as well as the wall crossing…

Gromov-Witten invariants for arbitrary projective varieties and arbitrary genus are constructed using the techniques from K. Behrend, B. Fantechi: The intrinsic normal cone.

We construct Gromov-Witten invariants of general symplectic manifolds.

A. Zinger defined reduced Gromov-Witten (GW) invariants and proved a comparison theorem of standard and reduced genus one GW invariants for every symplectic manifold (with all dimension). H. -L. Chang and J. Li provided a proof of the…

For each positive rational number $\epsilon$, we define $K$-theoretic $\epsilon$-stable quasimaps to certain GIT quotients $W\sslash G$. For $\epsilon>1$, this recovers the $K$-theoretic Gromov-Witten theory of $W\sslash G$ introduced in…

Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…

This paper is to construct unstable, Morita stable and stable bivariant algebraic Kasparov $K$-theory spectra of $k$-algebras. These are shown to be homotopy invariant, excisive in each variable $K$-theories. We prove that the spectra…

Polyfold theory, as developed by Hofer, Wysocki, and Zehnder, is a relatively new approach to resolving transversality issues that arise in the study of $J$-holomorphic curves in symplectic geometry. This approach has recently led to a…

We show that a holomorphic two-form $\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\mgn(X,\beta)$ to the locus where $\theta$ degenerates; it then enables us to define the…

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…

Let $(X,\om)$ be a symplectic manifold and $L$ be a Lagrangian submanifold diffeomorphic to $S^n$, $\R\P^n$, or a Lens space of a certain type. Using the symplectic cut and symplectic sum constructions, we express the open Gromov-Witten…

Holomorphic 2-forms on K\"{a}hler surfaces lead to "Local Gromov-Witten invariants" of spin curves. This paper shows how to derive sum formulas for such local GW invariants from the sum formula for GW invariants of certain ruled surfaces.…

We study the structure of the higher genus Gromov-Witten theory of the total space $K\mathbb{P}^{n-1}$ of the canonical bundle of the projective space $\mathbb{P}^{n-1}$. We prove the finite generation property for the Gromov-Witten…