相关论文: Nonexistence of phantom categories on very general…

We show that blowups of the projective plane at points lying on a smooth cubic curve do not contain phantoms, provided the points are chosen in very general position on this curve.

There are no Noetherian or Artinian bounded t-structures on geometric phantom or quasi-phantom categories.

In this paper we give a construction of phantom categories, i.e. admissible triangulated subcategories in bounded derived categories of coherent sheaves on smooth projective varieties that have trivial Hochschild homology and trivial…

A phantom category is an admissible subcategory with vanishing Grothendieck group of the bounded derived category of coherent sheaves on a smooth projective variety. The goal of this paper is to study the abstract situation when such a…

We show that the fundamental group is not invariant under derived equivalence of smooth projective varieties.

We show that the quasicategory defined as the localization of the category of (simple) graphs at the class of A-homotopy equivalences does not admit colimits. In particular, we settle in the negative the question of whether the A-homotopy…

We prove that there is no non-trivial aoutoequvivalence of the categoryof schemes of finite type over $\mathbb{Q}$.

We prove that there is no d such that all finite projective planes can be represented by convex sets in R^d, answering a question of Alon, Kalai, Matousek, and Meshulam. Here, if P is a projective plane with lines l_1,...,l_n, a…

We apply an improvement of the Delsarte LP-bound to give a new proof of the non-existence of finite projective planes of order 6, and uniqueness of finite projective planes of order 7. The proof is computer aided, and it is also feasible to…

In this article, we give a counterexample to the Lefschetz hyperplane theorem for non-singular quasi-projective varieties. A classical result of Hamm-L\^{e} shows that Lefschetz hyperplane theorem can hold for hyperplanes in general…

A minifold is a smooth projective $n$-dimensional variety such that its bounded derived category of coherent sheaves $\D^b(X)$ admits a semi-orthogonal decomposition into an exceptional collection of $n+1$ exceptional objects. In this paper…

We prove the non-existence of special generic maps on complex projective space as our extended new result. Simplest special generic maps are Morse functions with exactly two singular points on spheres, or Morse functions in Reeb's theorem,…

We prove in most cases that a general smooth complete intersection in the projective space has no non-trivial automorphisms.

The quantum hyperplane section theorem is explained for nonnegative decomposable concavex bundle spaces over generalized flag manifolds.

We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…

We construct a universal phantom subcategory on the blow-up of the complex projective plane in 11 general points. This phantom subcategory is the orthogonal complement of a non-full exceptional collection of line bundles of maximal length.…

We prove there exist infinitely many inequivalent fusion categories whose Grothendieck rings do not admit any pseudounitary categorifications.

We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically, our examples do not…

The purpose of the article is to explain a new method to establish the existence of an exceptional collection of length three for a fake projective plane M with non-trivial automorphism group, related to a conjecture of…

We prove some lower bounds on certain nonegative twists of the canonical bundle of a subvariety of a generic hypersurface in projective space. In particular we prove that the generic sextic threefold contains no rational or elliptic curves…