Related papers: Categorical characterization of quadrics

In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…

We present a geometric theorem on a porism about cyclic quadrilaterals, namely the existence of an infinite number of cyclic quadrilaterals through four fixed collinear points once one exists. Also, a technique of proving such properties…

We investigate combinatorial aspects of exceptional sequences in the derived category of coherent sheaves on certain smooth and complete algebraic surfaces. We show that to any such sequence there is canonically associated a complete toric…

Building on the concept of a smooth DG algebra we define the notion of a smooth derived category. We the propose the definition of a categorical resolution of singularities. Our main example is the derived category $D(X)$ of quasi-coherent…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

We classify rational, irreducible quartic symmetroids in projective 3-space. They are either singular along a line or a smooth conic section, or they have a triple point or a tacnode.

We construct characteristic classes of smooth (Hamiltonian) fibrations as as fiber integrals of products of Pontriagin (or Chern) classes of vertical vector bundles over the total space of the universal fibration. We give explicit formulae…

We classify spherical conjugacy classes in a simple algebraic group over an algebraically closed field of good, odd characteristic.

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…

We classify special self-birational transformations of the smooth quadric threefold and fourfold, $Q^3$ and $Q^4$. It turns out that there is only one such example in each dimension. In the case of $Q^3$, it is given by the linear system of…

Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual…

We define a categorical birational invariant for minimal geometrically rational surfaces with a conic bundle structure over a perfect field via components of a natural semiorthogonal decomposition. Together with the similar known result on…

We study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.

We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.

We classify compact complex surfaces which contain a Zariski open subset whose universal covering is the cylinder DxC.

A characterisation of trivial 1-cohomology for a broad class of metric spaces is presented. The condition ties cohomology and connectedness properties of open sets.

In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal character sheaves. This constitutes a major step towards the…

Let X be a Fano manifold such that every rational curve in X has anticanonical degree at least the dimension of X. We prove that X is a projective space or a quadric.

A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in…

The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.