Related papers: Categorical characterization of quadrics

Let $R$ be a finite dimensional algebra of finite global dimension over a field $k$. In this paper, we will characterize a $k$-linear abelian category $\mathscr C$ such that $\mathscr C\cong \operatorname {tails} A$ for some graded right…

The purpose of this paper is to prove the following theorem. Let $X$ be a projective normal variety defined over an algebraically closed field of characteristic zero and let $\Omega_{X}^{1}\to L$ be a one-dimensional foliation on $X$. If…

This is a complete classification of the complex forms of quaternionic symmetric spaces

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

We work out properties of smooth projective varieties over a (not necessarily algebraically closed) field that admit collections of objects in the bounded derived category of coherent sheaves that are either full exceptional, or numerically…

We classify maximal quartic generalised projective special real curves up to equivalence. A maximal quartic generalised projective special real curve consists of connected components of the intersection of the hyperbolic points of a quartic…

Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.

A general problem in complex cobordism theory is to find useful representatives for cobordism classes. One particularly convenient class of complex manifolds consists of smooth projective toric varieties. The bijective correspondence…

We give a Belyi-type characterisation of smooth complete intersections of general type over $\mathbb{C}$ which can be defined over $\bar{\mathbb{Q}}$. Our proof uses the higher-dimensional analogue of the Shafarevich boundedness conjecture…

We study smoothness of toric quiver varieties. When a quiver $Q$ is defined with the identity dimension vector, the corresponding quiver variety is also a toric variety. So it has both fan representation and quiver representation. We work…

Smooth real cubic surfaces are birationally trivial (over $\R$) if and only if their real locus is connected or, equivalently, if and only if they have two skew real lines or two skew complex conjugate lines. In such a case a…

We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification…

We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.

We show the geometric syzygy conjecture in positive characteristic. Specifically, if C is a general smooth curve of genus g defined over an algebraically closed field of characteristic p, then all linear syzygy spaces are spanned by…

We classify fibrations by integral plane projective rational quartic curves whose generic fibre is regular but admits a non-smooth point that is a canonical divisor. These fibrations can only exist in characteristic two. The geometric…

We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.

For a smooth plane cubic $B$, we count curves $C$ of degree $d$ such that the normalizations of $C\backslash B$ are isomorphic to $\Bbb A^1$, for $d\leq7$ (for $d=7$ under some assumption). We also count plane rational quartic curves…

Given a smooth projective variety V of dimension n, one may say that V has motivic dimension less than d+1 if the cohomology of V comes from varieties of dimensions less than d+1 in some geometric way. In this paper, we show that a smooth…

We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter…

We give a projective proof of the butterfly porism for cyclic quadrilaterals and present a general reversion porism for polygons with an arbitrary number of vertices on a conic. We also investigate projective properties of the porisms.