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 …
Virtual pullbacks in Donaldson-Thomas theory of Calabi-Yau 4-folds
H Park - arXiv preprint arXiv:2110.03631, 2021 - arxiv.org
Recently, Oh and Thomas constructed algebraic virtual cycles for moduli spaces of sheaves
on Calabi-Yau 4-folds. The purpose of this paper is to provide a virtual pullback formula …
on Calabi-Yau 4-folds. The purpose of this paper is to provide a virtual pullback formula …
Orientations for DT invariants on quasi-projective Calabi–Yau 4-folds
A Bojko - Advances in Mathematics, 2021 - Elsevier
Abstract For a Calabi–Yau 4-fold (X, ω), where X is quasi-projective and ω is a nowhere
vanishing section of its canonical bundle KX, the (derived) moduli stack of compactly …
vanishing section of its canonical bundle KX, the (derived) moduli stack of compactly …
Virasoro constraints for moduli of sheaves and vertex algebras
In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten
theory with many new recent developments in the sheaf theoretic context. In this paper, we …
theory with many new recent developments in the sheaf theoretic context. In this paper, we …
Counting perverse coherent systems on Calabi–Yau 4-folds
Y Cao, Y Toda - Mathematische Annalen, 2023 - Springer
Nagao-Nakajima introduced counting invariants of stable perverse coherent systems on
small resolutions of Calabi–Yau threefolds and determined them on the resolved conifold …
small resolutions of Calabi–Yau threefolds and determined them on the resolved conifold …
Counting surfaces on Calabi-Yau 4-folds I: foundations
This is the first part in a series of papers on counting surfaces on Calabi-Yau 4-folds.
Besides the Hilbert scheme of 2-dimensional subschemes, we introduce\emph {two} types of …
Besides the Hilbert scheme of 2-dimensional subschemes, we introduce\emph {two} types of …
Rank DT theory from rank
S Feyzbakhsh, RP Thomas - arXiv preprint arXiv:2103.02915, 2021 - arxiv.org
Fix a Calabi-Yau 3-fold $ X $ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\i-
Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting …
Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting …
Tautological stable pair invariants of Calabi-Yau 4-folds
Y Cao, Y Toda - Advances in Mathematics, 2022 - Elsevier
Let X be a Calabi-Yau 4-fold and D a smooth divisor on it. We consider tautological complex
associated with L= OX (D) on the moduli space of Le Potier stable pairs and define its …
associated with L= OX (D) on the moduli space of Le Potier stable pairs and define its …
Wall-crossing for zero-dimensional sheaves and Hilbert schemes of points on Calabi--Yau 4-folds
A Bojko - arXiv preprint arXiv:2102.01056, 2021 - arxiv.org
Gross--Joyce--Tanaka arXiv: 2005.05637 proposed a wall-crossing conjecture for Calabi--
Yau fourfolds. Assuming that it holds, we prove the conjecture of Cao--Kool arXiv …
Yau fourfolds. Assuming that it holds, we prove the conjecture of Cao--Kool arXiv …
Wall-crossing for punctual Quot-schemes
A Bojko - arXiv preprint arXiv:2111.11102, 2021 - arxiv.org
We study punctual quot-schemes of torsion-free sheaves $ E_Y $ on smooth projective
curves, surfaces and Calabi--Yau fourfolds via their virtual geometry. Our goal is to give a …
curves, surfaces and Calabi--Yau fourfolds via their virtual geometry. Our goal is to give a …