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 …

[HTML][HTML] Canonical vertex formalism in DT theory of toric Calabi-Yau 4-folds

S Monavari - Journal of Geometry and Physics, 2022 - Elsevier
Motivated by previous computations of Y. Cao, M. Kool and the author, we propose square
roots and sign rules for the vertex and edge terms that compute Donaldson-Thomas …

Tetrahedron instantons in Donaldson-Thomas theory

N Fasola, S Monavari - arXiv preprint arXiv:2306.07145, 2023 - arxiv.org
Inspired by the work of Pomoni-Yan-Zhang in String Theory, we introduce the moduli space
of tetrahedron instantons as a Quot scheme and describe it as a moduli space of quiver …

The 4-fold Pandharipande–Thomas vertex

H Liu - Journal of Geometry and Physics, 2024 - Elsevier
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 …

Murphy's law on a fixed locus of the Quot scheme

RF Schmiermann - arXiv preprint arXiv:2307.16272, 2023 - arxiv.org
Let $ T:=\mathbb {G} _m^ d $ be the torus acting on the Quot scheme of points
$\coprod_n\mathrm {Quot} _ {\mathcal {O}^ r/\mathbb {A}^ d/\mathbb {Z}}^ n $ via the …

Hilbert schemes of points on Calabi–Yau 4-folds via wall-crossing

A Bojko - Advances in Mathematics, 2024 - Elsevier
Abstract Gross–Joyce–Tanaka [43] proposed a wall-crossing conjecture for Calabi–Yau
fourfolds. Assuming it, we prove the conjecture of Cao–Kool [14] for 0-dimensional sheaf …

Tetrahedron Instantons on Orbifolds

RJ Szabo, M Tirelli - arXiv preprint arXiv:2405.14792, 2024 - arxiv.org
Given a homomorphism $\tau $ from a finite group $\mathsf {\Gamma} $ to $\mathsf {SU}(4)
$ with image $\mathsf {\Gamma}^\tau $, we construct a cohomological gauge theory on a …

Counting surfaces on Calabi-Yau 4-folds II: - correspondence

Y Bae, M Kool, H Park - arXiv preprint arXiv:2402.06526, 2024 - arxiv.org
This is the second part in a series of papers on counting surfaces on Calabi-Yau 4-folds. In
this paper, we introduce $ K $-theoretic $\mathrm {DT},\mathrm {PT} _0,\mathrm {PT} _1 …

A degeneration formula of Donaldson-Thomas theory on Calabi-Yau 4-folds

Y Cao, G Zhao, Z Zhou - arXiv preprint arXiv:2402.16103, 2024 - arxiv.org
arXiv:2402.16103v1 [math.AG] 25 Feb 2024 Page 1 arXiv:2402.16103v1 [math.AG] 25 Feb 2024
A DEGENERATION FORMULA OF DONALDSON-THOMAS THEORY ON CALABI-YAU …

K-Theoretic Donaldson-Thomas Theory of and Factorization

F Thimm - arXiv preprint arXiv:2404.15820, 2024 - arxiv.org
We compute the equivariant K-theoretic Donaldson--Thomas invariants of $[\mathbb {C}^
2/\mu_r]\times\mathbb {C} $ using factorization and rigidity techniques. For this, we develop …