Recently, Nekrasov discovered a new “genus” for Hilbert schemes of points on C 4. We
extend its definition to Hilbert schemes of curves and moduli spaces of stable pairs, and …

This paper is concerned with a non-compact GIT quotient of a vector space, in the presence
of an abelian group action and an equivariant regular function (potential) on the quotient …

A bstract We study the counting problem of BPS D-branes wrapping holomorphic cycles of a
general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured …

A bstract We introduce a class of 4-dimensional crystal melting models that count the BPS
bound state of branes on toric Calabi-Yau 4-folds. The crystalline structure is determined by …

Let $ G $ be a finite subgroup of $\mathrm {SU}(4) $ such that its elements have age at most
one. In the first part of this paper, we define $ K $-theoretic stable pair invariants on a …

As an analogy to the Gopakumar–Vafa conjecture on CY 3-folds, Klemm–Pandharipande
defined GV type invariants on CY 4-folds using GW theory and conjectured their integrality …

Abstract The Gopakumar–Vafa type invariants on Calabi–Yau 4-folds (which are non-trivial
only for genus zero and one) are defined by Klemm–Pandharipande from Gromov–Witten …

We study rank $ r $ cohomological Donaldson-Thomas theory on a toric Calabi-Yau orbifold
of $\mathbb {C}^ 4$ by a finite abelian subgroup $\mathsf\Gamma $ of $\mathsf {SU}(4) …

In our previous paper with Maulik, we proposed a conjectural Gopakumar-Vafa (GV) type
formula for the generating series of stable pair invariants on Calabi-Yau (CY) 4-folds. The …

Abstract Using reduced Gromov–Witten theory, we define new invariants which capture the
enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are …