Related papers: Gopakumar-Vafa Invariants and Macdonald Formula

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 consider genus zero quasimap invariants of smooth projective targets of the form $V/\!/G$, where $V$ is a representation of a reductive group $G$. In particular we consider integrals of cohomology classes arising as characteristic…

We study perverse sheaves of categories their connections to classical algebraic geometry. We show how perverse sheaves of categories encode naturally derived categories of coherent sheaves on $\mathbb{P}^1$ bundles, semiorthogonal…

We consider the moduli space of the McKay quiver representations associated to the binary polyhedral groups G < SU(2) < SU(3). The derived category of such representations is equivalent to the derived category of coherent sheaves on the…

n this paper we define an invariant of a pair of 6 dimensional symplectic %optional manifold with vanishing 1st Chern class and its Lagrangian submanifold with vanishing Maslov index. This invariant is a function on the set of the path…

We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special…

There is a strong analogy between compact, torsion-free $G_2$-manifolds $(X,\varphi,*\varphi)$ and Calabi-Yau 3-folds $(Y,J,g,\omega)$. We can also generalize $(X,\varphi,*\varphi)$ to 'tamed almost $G_2$-manifolds' $(X,\varphi,\psi)$,…

In alignment with a programme by Donaldson and Thomas [DT], Thomas [Th] constructed a deformation invariant for smooth projective Calabi-Yau threefolds, which is now called the Donaldson-Thomas invariant, from the moduli space of…

This review gives an introduction to cohomological Donaldson-Thomas theory: the study of a cohomology theory on moduli spaces of sheaves on Calabi-Yau threefolds, and of complexes in 3-Calabi-Yau categories, categorifying their numerical DT…

Let $\pi : X \to B$ be an elliptically fibered threefold satisfying $c_3(T_X \otimes \omega_X)=0$. We conjecture that the $\pi$-relative generating series of Pandharipande-Thomas invariants of $X$ are quasi-Jacobi forms and satisfy two…

We define and compute higher rank analogs of Pandharipande-Thomas stable pair invariants in primitive classes for K3 surfaces. Higher rank stable pair invariants for Calabi-Yau threefolds have been defined by Sheshmani \cite{shesh1,shesh2}…

We enumerate topologically-inequivalent compact Calabi-Yau threefold hypersurfaces. By computing arithmetic and algebraic invariants and the Gopakumar-Vafa invariants of curves, we prove that the number of distinct simply connected…

In their papers published in 1993 and 1994, by expressing certain physical quantity in two distinct ways, Bershadsky-Cecotti-Ooguri-Vafa discovered a remarkable equivalence between Ray-Singer analytic torsion and elliptic instanton numbers…

We introduce the vertical \(\widehat{A}\)-cowaist, a codimension-one invariant for partitioned manifolds. It extends the concept of infinite vertical \(\widehat{A}\)-cowaist for bands to arbitrary partitioned manifolds, which may be…

In this paper we compute the gravitational couplings of the heterotic string compactified on $(K3\times T^2)/\mathbb{Z}_N$ and $E_8\times E_8$ and predict the Gopakumar Vafa invariants of the dual Calabi Yau manifold in presence of Wilson…

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 study the contribution of multiple covers of an irreducible rational curve C in a Calabi-Yau threefold Y to the genus 0 Gromov-Witten invariants in the following cases. (1) If the curve C has one node and satisfies a certain genericity…

This paper shows that the motivic BPS invariants associated to a noncommutative crepant resolution of a compound Du-Val singularity are controlled by the labelled Dynkin combinatorics appearing in the work of Iyama--Wemyss. In particular,…

We consider a $(2q+1)$-dimensional smooth manifold $M$ equipped with a $(q+1)$-dimensional, a priori non-integrable, distribution ${\cal D}$ and a $q$-vector field ${\bf T}=T_1\wedge\ldots\wedge T_q$, where $\{T_i\}$ are linearly…

In this paper, we investigate Keller's deformed Calabi--Yau completion of the derived category of coherent sheaves on a smooth variety. In particular, for an $n$-dimensional smooth variety $Y$, we describe the derived category of the total…