Related papers: Semi-orthogonal decomposition and smoothing
We develop the method of inducing semiorthogonal decompositions of projective varieties with isolated rational singularities from those of small resolutions of singularities, which generalizes semiorthogonal decompositions for singular…
We embed several copies of the derived category of a quiver and certain line bundles in the derived category of an associated moduli space of representations, giving the start of a semiorthogonal decomposition. This mirrors the…
We study the derived category of coherent sheaves on various versions of moduli space of vector bundles on curves by the Borel-Weil-Bott theory for loop groups and $\Theta$-stratification, and construct a semiorthogonal decomposition with…
In this paper we investigate homologically finite-dimensional objects in the derived category of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd-closedness, and the Gorenstein property for…
We consider the deformation spaces of some singular product-quotient surfaces $X=(C_1 \times C_2)/G$, where the curves $C_i$ have genus 3 and the group $G$ is isomorphic to $\mathbb{Z}_4$. As a by-product, we give a new construction of…
We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived…
We define a categorical action of the shifted quantum loop group of $\mathfrak{sl}_2$ on the derived categories of Quot schemes of finite length quotient sheaves on a smooth projective curve. As an application, we obtain a semi-orthogonal…
Let U be the tautological subbundle on the Grassmannian $\mathrm{Gr}(k, n)$. There is a natural morphism $\mathrm{Tot}(U) \to \mathbb{A}^n$. Using it, we give a semiorthogonal decomposition for the bounded derived category…
To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…
We prove a relative version of the fact that semiorthogonal decompositions of the bounded derived category of coherent sheaves are strongly constrained by the base locus of the canonical linear system. As an application we prove that the…
Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$…
We establish some properties of the derived category of torus-equivariant coherent sheaves on a split toric stack bundle. Our main result is a semi-orthogonal decomposition of such a category.
We calculate a semi-orthogonal decomposition of the bounded derived category of coherent sheaves on P(1,1,1,3) using a tilting bundle.
We consider semi-orthogonal decompositions of derived categories for 3-dimensional projective varieties in the case when the varieties have ordinary double points.
We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…
We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived…
For any admissible subcategory of the bounded derived category of coherent sheaves on a smooth proper variety, we prove that sections of the canonical bundle impose a strong constraint on the supports of the objects of the subcategory or…
We show that the categorical action of the shifted $q=0$ affine algebra can be used to construct semiorthogonal decomposition on the weight categories. In particular, this construction recovers Kapranov's exceptional collection when the…
In this article, we investigate semi-orthogonal decompositions of the symmetric products of dg-enhanced triangulated categories. Given a semi-orthogonal decomposition $\mathcal{D}=\langle \mathcal{A}, \mathcal{B} \rangle$, we construct…
Let $\mathcal{X}$ be a smooth Deligne-Mumford stack which is generically a scheme and has quasi-projective coarse moduli. If $\mathcal{X}$ has elementary Abelian 2-group stabilizers and the coarse moduli of the inertia stack is smooth, we…