Related papers: Gopakumar-Vafa invariants via vanishing cycles
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…
The multi-Banana configuration $\widehat{F}_{mb}$ is a local Calabi-Yau threefold of Schoen type. Namely, $\widehat{F}_{mb}$ is a conifold resolution of $\widehat{I}_v \times_{\bf{D}} \widehat{I}_w$, where $\widehat{I}_v \to {\bf{D}}$ is an…
We show the existence of semiorthogonal decompositions (SOD) of Pandharipande-Thomas (PT) stable pair moduli spaces on Calabi-Yau 3-folds with irreducible curve classes, assuming relevant moduli spaces are non-singular. The above result is…
We formulate and prove the Remodeling Conjecture with descendants, which is a version of all-genus equivariant descendant mirror symmetry for semi-projective toric Calabi-Yau 3-orbifolds with integral structures. We construct an isomorphism…
We first construct a derived equivalence between a small crepant resolution of an affine toric Calabi-Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence we establish a wall-crossing formula for the…
We study equivariant Gromov-Witten invariants and quantum cohomology in GKM theory. Building on the localization formula, we prove that the resulting expression is independent of the choice of compatible connection, and provide an…
Let $(F,J,\omega)$ be an almost K\"ahler manifold, $\alpha$ a $J$-holomorphic action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup of $\hat K$ which leaves $\omega$ invariant. We introduce gauge theoretical…
We construct the Gromov-Witten invariants of moduli of stable morphisms to $\Pf$ with fields. This is the all genus mathematical theory of the Guffin-Sharpe-Witten model, and is a modified twisted Gromov-Witten invariants of $\Pf$. These…
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…
Donaldson-Thomas theory on a Calabi-Yau can be described in terms of a certain six-dimensional cohomological gauge theory. We introduce a certain class of defects in this gauge theory which generalize surface defects in four dimensions.…
We use a topological framework to study descendent Gromov-Witten theory in higher genus, non-toric settings. Two geometries are considered: surfaces of general type and the Enriques Calabi-Yau threefold. We conjecture closed formulas for…
We show a version of the DT/PT correspondence relating local curve counting invariants, encoding the contribution of a fixed smooth curve in a Calabi-Yau threefold. We exploit a local study of the Hilbert-Chow morphism about the cycle of a…
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…
In this paper, we propose a definition of genus one real Gromov-Witten invariants for certain symplectic manifolds with real a structure, including Calabi-Yau threefolds, and use equivariant localization to calculate certain genus one real…
Based on computations of Pandharipande, Zinger proved that the Gopakumar-Vafa BPS invariants $\mathrm{BPS}_{A,g}(X,\omega)$ for primitive Calabi-Yau classes and arbitrary Fano classes $A$ on a symplectic $6$-manifold $(X,\omega)$ agree with…
We introduce marked relative Pandharipande-Thomas (PT) invariants for a pair $(X,D)$ of a smooth projective threefold and a smooth divisor. These invariants are defined by integration over the moduli space of $r$-marked stable pairs on…
We rederive a relation between the genus-one GW-invariants of a quintic threefold in $\Pf$ and the genus-zero and genus-one GW-invariants of $\Pf$. In contrast to the more general derivation in a separate paper, the present derivation…
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…
In this paper, we study non-commutative projective schemes whose associated non-commutative graded algebras are finite over their centers. We study their moduli spaces of stable sheaves, and construct a symmetric obstruction theory in the…
We present a method to construct the extended K\"ahler cone of any Calabi-Yau threefold by using Gopakumar-Vafa invariants to identify all geometric phases that are related by flops or Weyl reflections. In this way we obtain the K\"ahler…