Related papers: Logarithmic Gromov-Witten theory with expansions
We use Gromov-Witten theory to study rational curves in holomorphic symplectic varieties. We present a numerical criterion for the existence of uniruled divisors swept out by rational curves in the primitive curve class of a very general…
In this paper we exploit the geometric approach to the virtual fundamental class, due to Fukaya-Ono and Li-Tian, to compare the virtual fundamental classes of stable maps to a symplectic manifold and a symplectic submanifold whenever all…
For $X$ a smooth projective variety and $D=D_1+\ldots+D_n$ a simple normal crossings divisor, we establish a precise cycle-level correspondence between the genus zero local Gromov-Witten theory of the bundle $\oplus_{i=1}^n…
We show that, after the change of variables $q=e^{iu}$, refined floor diagrams for $\mathbb{P}^2$ and Hirzebruch surfaces compute generating series of higher genus relative Gromov-Witten invariants with insertion of a lambda class. The…
In this paper we use the approach of Ruan and Li-Ruan to construct virtual neighborhoods and show that the Gromov-Witten invariants can be defined as an integral over top strata of virtual neighborhood. We prove that the invariants defined…
We represent stationary descendant Gromov-Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of large degree behaviour of stationary descendant…
This research announcement discusses our results on Gromov-Witten theory of root gerbes. A complete calculation of genus 0 Gromov-Witten theory of $\mu_{r}$-root gerbes over a smooth base scheme is obtained by a direct analysis of virtual…
We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold…
We show that the moduli space of stable n-pointed rational curves can be flatly degenerated to a projective toric variety. We arrive at this by showing that the Chow quotients of the Grassmannians admit toric degenerations, which in turn,…
Motivated by the real version of the Gopakumar-Vafa conjecture for 3-folds, the authors introduced in [GI] the notion of local real Gromov-Witten invariants associated to local 3-folds over Real curves. This article is devoted to the proof…
Let $\ix$ be a smooth Deligne-Mumford stack over the complex numbers. One can define twisted orbifold Gromov-Witten invariants of $\ix$ by considering multiplicative invertible characteristic classes of various bundles on the moduli spaces…
We extend B. Hassett's theory of weighted stable pointed curves ([Has03]) to weighted stable maps. The space of stability conditions is described explicitly, and the wall-crossing phenomenon studied. This can be considered as a non-linear…
The first part of this work constructs real positive-genus Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the second part studies the orientations on the moduli spaces of real maps used in…
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…
Using the global Kuranishi charts constructed in \cite{HS22}, we define gravitational descendants and equivariant Gromov-Witten invariants for general symplectic manifolds. We prove that that these invariants, equivariant and…
In this paper, we directly derive generalized mirror transformation of projective hypersurfaces up to degree 3 genus 0 Gromov-Witten invariants by comparing Kontsevich localization formula with residue integral representation of the virtual…
In this thesis we study the relation between scattering diagrams and deformations of holomorphic pairs, building on a recent work of Chan--Conan Leung--Ma. The new feature is the extended tropical vertex group where the scattering diagrams…
Given a closed symplectic manifold $X$, we construct Gromov-Witten-type invariants valued both in (complex) $K$-theory and in any complex-oriented cohomology theory $\mathbb{K}$ which is $K_p(n)$-local for some Morava $K$-theory $K_p(n)$.…
The goal of this paper is to give a general theory of logarithmic Gromov-Witten invariants. This gives a vast generalization of the theory of relative Gromov-Witten invariants introduced by Li-Ruan, Ionel-Parker, and Jun Li, and completes a…
Gromov-Witten invariants of weighted projective planes and Euler characteristics of moduli spaces of representations of bipartite quivers are related via the tropical vertex, a group of formal automorphisms of a torus. On the Gromov-Witten…