Counting sheaves on Calabi–Yau 4-folds, I

J Oh, RP Thomas - Duke Mathematical Journal, 2023 - projecteuclid.org
Borisov and Joyce constructed a real virtual cycle on compact moduli spaces of stable
sheaves on Calabi–Yau 4-folds, using derived differential geometry. We construct an …

Noncommutative instantons in diverse dimensions

RJ Szabo, M Tirelli - The European Physical Journal Special Topics, 2023 - Springer
This is a mini-review about generalized instantons of noncommutative gauge theories in
dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their …

Cohomological Hall algebras, vertex algebras and instantons

M Rapčák, Y Soibelman, Y Yang, G Zhao - … in Mathematical Physics, 2020 - Springer
We define an action of the (double of) Cohomological Hall algebra of Kontsevich and
Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We …

Gauge origami and quiver W-algebras

T Kimura, G Noshita - Journal of High Energy Physics, 2024 - Springer
A bstract We explore the quantum algebraic formalism of the gauge origami system in ℂ 4,
where D2/D4/D6/D8-branes are present. We demonstrate that the contour integral formulas …

Enumerative invariants and wall-crossing formulae in abelian categories

D Joyce - arXiv preprint arXiv:2111.04694, 2021 - arxiv.org
Enumerative invariants in Algebraic Geometry'count'$\tau $-(semi) stable objects $ E $ with
fixed topological invariants $[E]= a $ in some geometric problem, using a virtual class $[{\cal …

Vafa-Witten invariants for projective surfaces I: stable case

Y Tanaka, RP Thomas - arXiv preprint arXiv:1702.08487, 2017 - arxiv.org
On a polarised surface, solutions of the Vafa-Witten equations correspond to certain
polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a …

Magnificent four

N Nekrasov - Annales de l'Institut Henri Poincaré D, 2020 - ems.press
Magnificent four Page 1 Ann. Inst. Henri Poincaré Comb. Phys. Interact. 7 (2020), 505–534 DOI
10.4171/AIHPD/93 Magnificent four Nikita Nekrasov Abstract. We present a statistical …

K-Theoretic DT/PT Correspondence for Toric Calabi–Yau 4-Folds

Y Cao, M Kool, S Monavari - Communications in Mathematical Physics, 2022 - Springer
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 …

Quasimaps to quivers with potentials

Y Cao, G Zhao - arXiv preprint arXiv:2306.01302, 2023 - arxiv.org
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 …

[HTML][HTML] Orientability of moduli spaces of Spin (7)-instantons and coherent sheaves on Calabi–Yau 4-folds

Y Cao, J Gross, D Joyce - Advances in Mathematics, 2020 - Elsevier
Abstract Suppose (X, Ω, g) is a compact Spin (7)-manifold, eg a Riemannian 8-manifold with
holonomy Spin (7), or a Calabi–Yau 4-fold. Let G be U (m) or SU (m), and P→ X be a …