Related papers: Categorical resolutions of cuspidal singularities

Using a relative version of Auslander's formula, we give a functorial approach to show that the bounded derived category of every Artin algebra admits a categorical resolution. This, in particular, implies that the bounded derived…

In this note, we introduce monoidal subcategories of the tensor category of finite-dimensional representations of a simply-laced quantum affine algebra, parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of types A and…

We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi…

We provide descriptions of the derived categories of degree $d$ hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of a well-known theorem of Orlov. Using a local generator and…

Let $A$ be a Noetherian ring of dimension $d$ and let $\mathcal{D}^b(A)$ be the bounded derived category of $A$. Let $\mathcal{D}_i^b(A)$ denote the thick subcategory of $\mathcal{D}^b(A)$ consisting of complexes $\mathbf{X}_\bullet$ with…

We consider a surface that admits a $\mathbb{Q}$-Gorenstein degeneration to a cyclic quotient singularity $\frac{1}{dn^2}(1,dna-1)$. Under several technical assumptions, we construct $d$ exceptional vector bundles of rank $n$ which are…

We show how the classification of simple singularities of functions can be reduced directly, not using the normal forms, to the classification of irreducible Weyl groups. We also prove that the class of a singularity in its local algebra…

Let X be a singular affine normal variety with coordinate ring R and assume that there is an R-order admitting a stability structure such that the scheme of relevant semistable representations is smooth, then we construct a partial…

Let $\mathcal{A}$ be an abelian category. Denote by $\mathrm{D}^{b}(\mathcal{A})$ the bounded derived category of $\mathcal{A}$. In this paper, we investigate the lower bounds for the levels of objects in $\mathrm{D}^{b}(\mathcal{A})$ with…

Consider a space X with the singular locus of positive dimension, Z=Sing(X). Suppose both Z and X are locally complete intersections at each point. The transversal type of X along Z is generically constant but at some points of Z it…

In this article we obtain a rigid isotopy classification of generic pointed quartic curves $(A,p)$ in $\mathbb{R}\mathbb{P}^{2}$ by studying the combinatorial properties of dessins. The dessins are real versions, proposed by S. Orevkov, of…

We introduce a novel commutative C*-algebra $C_\mathcal{R}(X)$ of functions on a symplectic vector space $(X,\sigma)$ admitting a complex structure, along with a strict deformation quantization that maps a dense subalgebra of…

This paper is devoted to a very classical problem that can be summarized as follows: let S be a non singular compact complex surface, f:S --> P^2 a finite morphism having simple branching, B the branch curve: to what extent does B determine…

We determine explicitly the irreducible components of the singular locus of any Schubert variety for GL_n(K), K being an algebraically closed field of arbitrary characteristic. We also describe the generic singularities along these…

As proved recently in [PT], for varieties $X^{r+1}\subset \mathbb P^N$ such that through $n\geq 2$ general points there passes an irreducible curve $C$ of degree $\delta\geq n-1$ we have $N\leq \pi(r,n,\delta+r(n-1)+2)$, where $\pi(r,n,d)$…

We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In…

We use recollement and HRS-tilt to describe bounded t-structures on the bounded derived category $\mathcal{D}^b(\mathbb{X})$ of coherent sheaves over a weighted projective line $\mathbb{X}$ of virtual genus $\leq 1$. We will see from our…

We study Verdier quotients of diverse homotopy categories of a full additive subcategory $\mathcal E$ of an abelian category. In particular, we consider the categories $K^{x,y}({\mathcal E})$ for $x\in\{\infty, +,-,b\}$, and…

Let $X$ denote the `conifold smoothing', the symplectic Weinstein manifold which is the complement of a smooth conic in $T^*S^3$, or equivalently the plumbing of two copies of $T^*S^3$ along a Hopf link. Let $Y$ denote the `conifold…

Let $X$ be a cubic fourfold that has only simple singularities and does not contain a plane. We prove that the Fano variety of lines on $X$ has the same analytic type of singularity as the Hilbert scheme of two points on a surface with only…