Related papers: Flop invariance of the topological vertex
We will establish the fermionic gluing principle of the topological vertex, that is, provided the framed ADKMV conjecture, the generating functions of the Gromov-Witten invariants of all toric Calabi-Yau threefolds are Bogoliubov transforms…
We compute certain open Gromov-Witten invariants for toric Calabi-Yau threefolds. The proof relies on a relation for ordinary Gromov-Witten invariants for threefolds under certain birational transformation, and a recent result of Kwokwai…
We define relative Gromov-Witten invariants and establish a general gluing theory of pseudo-holomorphic curves for symplectic cutting and contact surgery. Then, we use our general gluing theory to study the change of GW-invariants of…
Based on the large N duality relating topological string theory on Calabi-Yau 3-folds and Chern-Simons theory on 3-manifolds, M. Aganagic, A. Klemm, M. Marino and C. Vafa proposed the topological vertex (hep-th/0305132), an algorithm on…
We investigate Gromov-Witten invariants associated to exceptional classes for primitive birational contractions on a Calabi-Yau threefold X. It was observed in a previous paper that these invariants are locally defined, in that they can be…
The Gopakumar-Vafa invariants are numbers defined as certain linear combinations of the Gromov-Witten invariants. We prove that the GV invariants of a toric Calabi-Yau threefold are integers and that the invariants for high genera vanish.…
We propose a general theory of the Open Gromov-Witten invariant on Calabi-Yau three-folds. In this paper we construct the Open Gromov-Witten potential. The evaluation of the potential on its critical points leads to numerical invariants.
We develop a gluing algorithm for Gromov-Witten invariants of toric Calabi-Yau threefolds based on localization and gluing graphs. The main building block of this algorithm is a generating function of cubic Hodge integrals of special form.…
The BKMP conjecture (2006-2008), proposed a new method to compute closed and open Gromov-Witten invariants for every toric Calabi-Yau 3-folds, through a topological recursion based on mirror symmetry. So far, this conjecture had been…
We conjecture the existence of almost integer invariants governing the all-genus equivariant Gromov-Witten theory of Calabi-Yau fivefolds with a torus action. We prove the conjecture for skeletal, locally anti-diagonal torus actions by…
We compute the local Gromov-Witten invariants of the "closed vertex", that is, a configuration of three rational curves meeting in a single triple point in a Calabi-Yau threefold. The method is to express the local invariants of the vertex…
We study how Gromov-Witten invariants of projective 3-folds transform under a standard flop and a small extremal transition in the algebro-geometric setting from the recent development of algebraic relative Gromov-Witten theory and its…
We prove the transformation formula of Donaldson-Thomas (DT) invariants counting two dimensional torsion sheaves on Calabi-Yau 3-folds under flops. The error term is described by the Dedekind eta function and the Jacobi theta function, and…
The theory of the topological vertex was originally proposed by Aganagic, Klemm, Mari\~no and Vafa as a means to calculate open Gromov-Witten invariants of toric Calabi-Yau threefolds. In this paper, we place the topological vertex within…
The zeroth line bundle cohomology on Calabi-Yau three-folds encodes information about the existence of flop transitions and the genus zero Gromov-Witten invariants. We illustrate this claim by studying several Picard number 2 Calabi-Yau…
It has been proposed recently that the topological A-model string theory on local toric Calabi-Yau manifolds has a two parameter extension. Amplitudes of the two parameter topological strings can be computed using a diagrammatic method…
We construct a matrix model that reproduces the topological string partition function on arbitrary toric Calabi-Yau 3-folds. This demonstrates, in accord with the BKMP "remodeling the B-model" conjecture, that Gromov-Witten invariants of…
We compute the local Gromov-Witten invariants of certain configurations of rational curves in a Calabi-Yau threefold. These configurations are connected subcurves of the `minimal trivalent configuration', which is a particular tree of P^1's…
We present a mathematical proof of the Aganagic-Dijkgraaf-Klemm-Mari\~no-Vafa Conjecture proposed in 2006, which states that the generating function of the topological vertex, i.e., the generating function of the open Gromov-Witten…
We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm,…