Related papers: Categorical Torelli theorem for hypersurfaces

There are many four vertex type theorems appearing in the literature, coming in both smooth and discrete flavors. The most familiar of these is the classical theorem in differential geometry, which states that the curvature function of a…

We introduce and describe the $2$-category $\mathsf{Grt}_{\flat}$ of Grothendieck categories and flat morphisms between them. First, we show that the tensor product of locally presentable linear categories $\boxtimes$ restricts nicely to…

In this paper we give an effective criterion as to when a positive integer q is the order of an automorphism of a smooth hypersurface of dimension n and degree d, for every d>2, n>1, (n,d)\neq (2,4), and \gcd(q,d)=\gcd(q,d-1)=1. This allows…

In this paper by using the ring of real-valued continuous functions $C(X)$, we prove a theorem in profinite spaces which states that for a compact Hausdorff space $X$, the set of its connected components $X/_{\sim}$ endowed with some…

If a Quillen model category can be specified using a certain logical syntax (intuitively, ``is algebraic/combinatorial enough''), so that it can be defined in any category of sheaves, then the satisfaction of Quillen's axioms over any site…

The number of apparent double points of an irreducible projective variety $X$ of dimension $n$ in $\mathbb{P}^{2n+1}$ is the number of secant lines to $X$ passing through a general point of $\mathbb{P}^{2n+1}$. This classical notion dates…

Using the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree $d \in \{2,3,4,5\}$ and crepant categorical resolutions of the nontrivial…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

Let $k$ be an algebraically closed field and let $b$ and $n$ be integers with $n\geq 3$ and $1\leq b \leq n-1.$ Consider the moduli space $X$ of hypersurfaces in $\mathbb{P}^n_k$ of fixed degree $l$ whose singular locus is at least…

A once-extended d-dimensional topological field theory Z is a symmetric monoidal functor (taking values in a chosen target symmetric monoidal (infty,2)-category) assigning values to (d-2)-manifolds, (d-1)-manifolds, and d-manifolds. We show…

We construct and study a new family of TQFTs based on nilpotent highest weight representations of quantum sl(2) at a root of unity indexed by generic complex numbers. This extends to cobordisms the non-semi-simple invariants defined in…

We prove a reconstruction theorem \`a la Calabrese-Groechenig for the moduli space parametrizing skyscraper sheaves on a smooth projective variety when these are considered as a system of points in the dg category of perfect complexes on…

Following and developing ideas of R. Karasev (Covering dimension using toric varieties, arXiv:1307.3437), we extend the Lebesgue theorem (on covers of cubes) and the Knaster-Kuratowski-Mazurkiewicz theorem (on covers of simplices) to…

In 1972, E. P. Senkin generalized the celebrated theorem of A. V. Pogorelov on unique determination of compact convex surfaces by their intrinsic metrics in the Euclidean 3-space $E^3$ to higher dimensional Euclidean spaces $E^{n+1}$ under…

Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let U be an open subset whose complement has codimension at least 2. We extend the Deligne-Bezrukavnikov theory of perverse coherent sheaves…

We give sharp lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and…

In this paper, we study necessary and sufficient conditions for the existence of categorical universal coverings using open covers of a given space $X$. As some applications, first we present a generalized version of the Shelah Theorem…

In this note we show that $k$-convex functions on $\Bbb R^n$ are twice differentiable almost everywhere for every positive integer $k>n/2$. This generalizes the classical Alexsandrov's theorem for convex functions.

Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of "parity sheaves", which are objects in the constructible derived category of sheaves with coefficients in…

We investigate a necessary condition for a compact complex manifold X of dimension n in order that its universal cover be the Cartesian product $C^n$ of a curve $C = \PP^1 or \HH$: the existence of a semispecial tensor $\omega$. A…