Related papers: Wall-crossing for Calabi-Yau fourfolds: framework,…
Gross-Joyce-Tanaka arXiv:2005.05637 proposed a wall-crossing conjecture for Calabi-Yau fourfolds. Assuming it, we prove the conjecture of Cao-Kool arXiv:1712.07347 for 0-dimensional sheaf-counting invariants on projective Calabi-Yau…
We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi--Yau categories arising from virtual cycles. The strategy follows ideas of Joyce's ``universal'' wall-crossing framework arXiv:2111.04694,…
In our previous paper with Maulik, we proposed a conjectural Gopakumar-Vafa (GV) type formula for the generating series of stable pair invariants on Calabi-Yau (CY) 4-folds. The purpose of this paper is to give an interpretation of the…
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 complete description of the virtual fundamental classes and their…
We introduce a higher rank analog of the Joyce-Song theory of stable pairs. Given a nonsingular projective Calabi-Yau threefold $X$, we define the higher rank Joyce-Song pairs given by ${O}^{r}_{X}(-n)\rightarrow F$ where $F$ is a pure…
The notion of limit stability on Calabi-Yau 3-folds is introduced by the author to construct an approximation of Bridgeland-Douglas stability conditions at the large volume limit. It has also turned out that the wall-crossing phenomena of…
In this paper, we introduce the notion of parabolic stable pairs on Calabi-Yau 3-folds and invariants counting them. By applying the wall-crossing formula developed by Joyce-Song, Kontsevich-Soibelman, we see that they are related to…
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 moduli spaces of stable pairs. We show that all three moduli…
In this paper, we introduce new enumerative invariants of curves on Calabi-Yau 3-folds via certain stable objects in the derived category of coherent sheaves. We introduce the notion of limit stability on the category of perverse coherent…
The invariants of rank 2 Joyce-Song semistable pairs over a Calabi-Yau threefold were computed in arXiv:1101.2252, using the wall-crossing formula of Joyce-Song and Kontsevich-Soibelman. Such wall-crossing computations often depend on the…
Nagao-Nakajima introduced counting invariants of stable perverse coherent systems on small resolutions of Calabi-Yau 3-folds and determined them on the resolved conifold. Their invariants recover DT/PT invariants and Szendr\"oi's…
Given an abelian category and a stability condition satisfying appropriate conditions, we define generalized $K$-theoretic invariants and prove that they satisfy wall-crossing formulas. For this, we introduce a new associative algebra…
We apply results on inducing stability conditions to local Calabi-Yau threefolds and obtain applications to Donaldson-Thomas (DT) theory. A basic example is the total space of the canonical bundle of $Z=\mathbb{P}^1\times \mathbb{P}^1$. We…
Let $X$ be a compact complex Calabi-Yau 4-fold. Under certain assumptions, we define Donaldson-Thomas type deformation invariants ($DT_{4}$ invariants) by studying moduli spaces of solutions to the Donaldson-Thomas equations on $X$. We also…
We study higher rank Donaldson-Thomas invariants of a Calabi-Yau 3-fold using Joyce-Song's wall-crossing formula. We construct quivers whose counting invariants coincide with the Donaldson-Thomas invariants. As a corollary, we prove the…
We provide a general framework for wall-crossing of equivariant K-theoretic enumerative invariants of appropriate moduli stacks $\mathfrak{M}$, by lifting Joyce's homological universal wall-crossing arXiv:2111.04694 to K-theory and to…
In this paper, we investigate the space of certain weak stability conditions on the triangulated category of D0-D2-D6 bound states on a smooth projective Calabi-Yau 3-fold. In the case of a quintic 3-fold, the resulting space is interpreted…
We describe wall-crossing for local, toric Calabi-Yau manifolds without compact four-cycles, in terms of free fermions, vertex operators, and crystal melting. Firstly, to each such manifold we associate two states in the free fermion…
The theory of stable pairs in the derived category yields an enumerative geometry of curves in 3-folds. We evaluate the equivariant vertex for stable pairs on toric 3-folds in terms of weighted box counting. In the toric Calabi-Yau case,…
The notion of d-critical loci was introduced by Joyce in order to give classical shadows of $(-1)$-shifted symplectic derived schemes. In this paper, we discuss birational geometry for d-critical loci, by introducing notions such as…