For a nonsingular projective 3-fold X, we define integer invariants virtually enumerating pairs
(C, D) where C⊂ X is an embedded curve and D⊂ C is a divisor. A virtual class is …

We prove that Donaldson-Thomas type invariants are equal to weighted Euler
characteristics of their moduli spaces. In particular, such invariants depend only on the …

In the past 20 years, compactifications of the families of curves in algebraic varieties X have
been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable …

A quasi-smooth derived enhancement of a Deligne–Mumford stack 𝒳 naturally endows 𝒳
with a functorial perfect obstruction theory in the sense of Behrend–Fantechi. We apply this …

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 …

We derive two multivariate generating functions for three-dimensional (3D) Young diagrams
(also called plane partitions). The variables correspond to a coloring of the boxes according …

We compute the motivic Donaldson–Thomas theory of the resolved conifold, in all chambers
of the space of stability conditions of the corresponding quiver. The answer is a product …

We verify a recent conjecture of Kenyon/Szendrői by computing the generating function for
pyramid partitions. Pyramid partitions are closely related to Aztec Diamonds; their …

The purpose of this paper is twofold. First we give a survey on the recent developments of
curve counting invariants on Calabi–Yau 3-folds, for example, Gromov–Witten theory …

Let G be a polyhedral group, namely a finite subgroup of SO (3). Nakamura's G-Hilbert
scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity ℂ 3/G …