Related papers: Higher rank stable pairs on K3 surfaces

The conjectural equivalence of curve counting on Calabi-Yau 3-folds via stable maps and stable pairs is discussed. By considering Calabi-Yau 3-folds with K3 fibrations, the correspondence naturally connects curve and sheaf counting on K3…

We study moduli space of holomorphic triples $E_{1}\xrightarrow{\phi} E_{2}$, composed of torsion-free sheaves $E_{i}, i=1,2$ and a holomorphic mophism between them, over a smooth complex projective surface $S$. The triples are equipped…

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…

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 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)…

We study the virtual geometry of the moduli spaces of curves and sheaves on K3 surfaces in primitive classes. Equivalences relating the reduced Gromov-Witten invariants of K3 surfaces to characteristic numbers of stable pairs moduli spaces…

We introduce a higher rank analog of the Joyce-Song theory of stable pairs. Given a nonsingular projective Calabi-Yau threefold $X$, we define the higher rank Joyce-Song pairs given by ${O}^{r}_{X}(-n)\rightarrow F$ where $F$ is a pure…

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…

For a Calabi-Yau 3-fold $X$, we explicitly compute the Donaldson-Thomas type invariant counting pairs $(F, V)$, where $F$ is a zero-dimensional coherent sheaf on $X$ and $V\subset F$ is a two dimensional linear subspace, which satisfy a…

Let M(v) be the moduli of stable sheaves on K3 surfaces X of Mukai vector v. If v is primitive, than it is expected that M(v) is deformation equivalent to some Hilbert scheme and weight two hogde structure can be described by H^*(X,Z).…

We study threefolds fibred by K3 surfaces admitting a lattice polarization by a certain class of rank 19 lattices. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the…

We prove the KKV conjecture expressing Gromov-Witten invariants of K3 surfaces in terms of modular forms. Our results apply in every genus and for every curve class. The proof uses the Gromov-Witten/Pairs correspondence for K3-fibered…

We prove the rationality of the descendent partition function for stable pairs on nonsingular toric 3-folds. The method uses a geometric reduction of the 2- and 3-leg descendent vertices to the 1-leg case. As a consequence, we prove the…

In this paper, we introduce the notion of parabolic stable pairs on Calabi-Yau 3-folds and invariants counting them. By applying the wall-crossing formula developed by Joyce-Song, Kontsevich-Soibelman, we see that they are related to…

Let $G$ be a finite subgroup of $\mathrm{SU}(4)$ whose elements have age not larger than one. In the first part of this paper, we define $K$-theoretic stable pair invariants on the crepant resolution of the affine quotient $\mathbb{C}^4/G$,…

We give a conjectural but full and explicit description of the (K-theoretic) equivariant vertex for Pandharipande--Thomas stable pairs on toric Calabi--Yau 4-folds, by identifying torus-fixed loci as certain quiver Grassmannians and…

Recently, Cao-Maulik-Toda defined stable pair invariants of a compact Calabi-Yau 4-fold $X$. Their invariants are conjecturally related to the Gopakumar-Vafa type invariants of $X$ defined using Gromov-Witten theory by Klemm-Pandharipande.…

For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space…

We develop a theory of Gopakumar-Vafa (GV) invariants for a Calabi-Yau threefold (CY3) $X$ which is equipped with an involution $\imath$ preserving the holomorphic volume form. We define integers $n_{g,h}(\beta) $ which give a virtual count…

In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau--Zaslow (capturing the Euler…