Related papers: Higher rank stable pairs and virtual localization
This work develops new ideas and tools to establish wall-crossing in Calabi-Yau four categories as originally conjectured by Gross-Joyce-Tanaka. In the process, I set up some necessary new language, including a natural refinement of Joyce's…
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its…
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…
We review the ghost-free four-derivative terms for chiral superfields in $\mathcal{N}=1$ supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar…
We analyze the relationship between two compactifications of the moduli space of maps from curves to a Grassmannian: the Kontsevich moduli space of stable maps and the Marian--Oprea--Pandharipande moduli space of stable quotients. We…
In this paper, we explore the virtual technique that is very useful in studying moduli problem from differential geometric point of view. We introduce a class of new objects "virtual manifolds/orbifolds", on which we develop the integration…
In earlier work, the author introduced a method for constructing a Frobenius categorification of a cluster algebra with frozen variables by starting from the data of an internally Calabi-Yau algebra, which becomes the endomorphism algebra…
We introduce a non-associative model for the Hilbert scheme of points in arbitrary dimension. We define a smooth ambient space, which we call the non-associative Hilbert scheme, containing the classical nested Hilbert scheme…
For $g,n\geq 0$ a 3-dimensional Calabi-Yau $A_\infty$-category $\mathcal C_{g,n}$ is constructed such that a component of the space of Bridgeland stability conditions, $\mathrm{Stab}(\mathcal C_{g,n})$, is a moduli space of quadratic…
We study moduli stabilization of the F-theory compactified on an elliptically fibered Calabi-Yau fourfold. Our setup is based on the mirror symmetry framework including brane deformations. The complex structure moduli dependence of the…
Holomorphic gauge fields in N=1 supersymmetric heterotic compactifications can constrain the complex structure moduli of a Calabi-Yau manifold. In this paper, the tools necessary to use holomorphic bundles as a mechanism for moduli…
We describe what it means for an algebra to be internally d-Calabi-Yau with respect to an idempotent. This definition abstracts properties of endomorphism algebras of (d-1)-cluster-tilting objects in certain stably (d-1)-Calabi-Yau…
In this note we consider M-theory compactified on a warped Calabi-Yau fourfold including the eight-derivative terms in the eleven-dimensional action known in the literature. We dimensionally reduce this theory on geometries with one Kahler…
We consider the moduli space of stable torsion free sheaves of any rank on a smooth projective threefold. The singularity set of a torsion free sheaf is the locus where the sheaf is not locally free. On a threefold it has dimension $\leq…
In this paper, we show that the presence of gauge fields in heterotic Calabi-Yau compacitifications causes the stabilisation of some, or all, of the complex structure moduli of the Calabi-Yau manifold while maintaining a Minkowski vacuum.…
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…
Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental…
Kontsevich and Soibelman introduced a notion of orientation data on Calabi-Yau category. It can be viewed as a consistent choice of spin structure on moduli space of objects in the given category. The orientation data plays an important…
We develop a theory of complex Kuranishi structures on projective schemes. These are sufficiently rigid to be equivalent to weak perfect obstruction theories, but sufficiently flexible to admit global complex Kuranishi charts. We apply the…
Mirror symmetry suggests that on a Calabi-Yau 3-fold moduli spaces of stable bundles, especially those with degree zero and indivisible Chern class, might be smooth (i.e. unobstructed, though perhaps of too high a dimension). This is…