Counting sheaves on Calabi–Yau 4-folds, I
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 …
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 …
dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their …
Cohomological Hall algebras, vertex algebras and instantons
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 …
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 …
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 …
fixed topological invariants $[E]= a $ in some geometric problem, using a virtual class $[{\cal …
Vafa-Witten invariants for projective surfaces I: stable case
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 …
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 …
10.4171/AIHPD/93 Magnificent four Nikita Nekrasov Abstract. We present a statistical …
K-Theoretic DT/PT Correspondence for Toric Calabi–Yau 4-Folds
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 …
extend its definition to Hilbert schemes of curves and moduli spaces of stable pairs, and …
Quasimaps to quivers with potentials
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 …
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
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 …
holonomy Spin (7), or a Calabi–Yau 4-fold. Let G be U (m) or SU (m), and P→ X be a …