Related papers: Gopakumar-Vafa Invariants and Macdonald Formula
We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a…
Let $X$ be a Calabi-Yau 4-fold and $D$ a smooth divisor on it. We consider tautological complex associated with $L=\mathcal{O}_X(D)$ on the moduli space of Le Potier stable pairs and define its counting invariant by integrating the Euler…
We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The stability depends on the choice of a component (= a chamber)…
The Castelnuovo bound conjecture, which is proposed by physicists, predicts an effective vanishing result for Gopakumar-Vafa invariants of Calabi-Yau 3-folds of Picard number one. Previously, it is only known for a few cases and all the…
In this paper, we introduce new enumerative invariants of curves on Calabi-Yau 3-folds via certain stable objects in the derived category of coherent sheaves. We introduce the notion of limit stability on the category of perverse coherent…
We prove a closed formula for leading Gopakumar- Vafa BPS invariants of local Calabi-Yau geometries given by the canonical line bundles of toric Fano surfaces. It shares some similar features with Goettsche-Yau-Zaslow formula: Connection…
We propose a combined mechanism to realize both winding inflation and de Sitter uplifts. We realize the necessary structure of competing terms in the scalar potential not via tuning the vacuum expectation values of the complex structure…
Two 3-fold flops are exhibited, both of which have precisely one flopping curve. One of the two flops is new, and is distinct from all known algebraic D4-flops. It is shown that the two flops are neither algebraically nor analytically…
The conifold is a basic example of a noncompact Calabi-Yau threefold that admits a simple flop, and in M-theory, gives rise to a 5d hypermultiplet at low energies, realized by an M2-brane wrapped on the vanishing sphere. We develop a novel…
This paper contains a preliminary study of the monodromy of certain fourth order differential equations, that were called of Calabi-Yau type in math.NT/0402386. Some of these equations can be interpreted as the Picard-Fuchs equations of a…
We prove Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds. It's also proved that the local Gopakumar-Vafa invariants of a given class at large genus vanish.
We calculate the topological string amplitudes of Calabi-Yau toric threefolds corresponding to 4D, N=2, SU(2) gauge theory with N_f=0,1,2,3,4 fundamental hypermultiplets by using the method of the geometric transition and show that they…
Motivated by S-duality modularity conjectures in string theory, we define new invariants counting a restricted class of 2-dimensional torsion sheaves, enumerating pairs $Z\subset H$ in a Calabi-Yau threefold X. Here H is a member of a…
We study a conjectural relationship among Donaldson-Thomas type invariants on Calabi-Yau 3-folds counting torsion sheaves supported on ample divisors, ideal sheaves of curves and Pandharipande-Thomas's stable pairs. The conjecture is a…
After Bershadsky-Cecotti-Ooguri-Vafa, we introduce an invariant of Calabi-Yau threefolds, which we call the BCOV invariant and which we obtain using analytic torsion. We give an explicit formula for the BCOV invariant as a function on the…
In Type IIA compactified on a Calabi-Yau threefold, the genus zero and one terms of the Gopakumar-Vafa (GV) formula describe F-terms that are related to genus zero and one topological amplitudes. While for higher-genus terms $\mathcal{F}_g,…
The Gopakumar-Vafa conjecture predicts that the BPS invariants of a symplectic 6-manifold, defined in terms of the Gromov-Witten invariants, are integers and all but finitely many vanish in every homology class. The integrality part of this…
We define an integer-valued virtual count of embedded pseudo-holomorphic curves of two times a primitive homology class and arbitrary genus in symplectic Calabi--Yau $3$-folds, which can be viewed as an extension of Taubes' Gromov…
We compute the Donaldson-Thomas invariants for two types of Calabi-Yau 3-folds. These invariants are associated to the moduli spaces of rank-2 Gieseker semistable sheaves. None of the sheaves are locally free, and their double duals are…
In this paper, we investigate the space of certain weak stability conditions on the triangulated category of D0-D2-D6 bound states on a smooth projective Calabi-Yau 3-fold. In the case of a quintic 3-fold, the resulting space is interpreted…