Related papers: Addendum to: Generically split projective homogene…
We show that local complete intersection subvarieties of smooth projective varieties, which have partially ample normal bundle, possess the G2-property. This generalizes results of Hartshorne and B\u{a}descu-Schneider.
We obtain a Bogomolov type of result for the additive group scheme in characteristic $p$. Our result is equivalent with a Bogomolov theorem for Drinfeld modules defined over a finite field.
The main result of [HL] (Annals of Math. 102 (1975), 223--290) gives a characterization of the boundaries of complex subvarieties in C^n. An application of this result concerning pseudoconvexity, namely Theorem 10.4 in [HL], is amplified.
We study subvarieties of a general projective degree $d$ hypersurface $X_d\subset \mathbf P^n$. Our main theorem, which improves previous results of L. Ein and C. Voisin, implies in particular the following sharp corollary: any subvariety…
We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type. The paper covers the following topics: construction of integral models, their possible moduli…
We show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some…
We list the irreducible reduced and not degenerate normal projective varieties $X\subset\mathbb{P}^N$ of dimension $n$ and degree five defined over an algebraically closed field $k$ of char$(k) = 0$. In the smooth case, or when $n = 2$, we…
In this paper, we shall generalize the theory of mixed Hodge structures due to Deligne and obtain a subcategory GMHS in the category of mixed Hodge structures such that we have Ext_{GMHS}^2(Q,-)\not=0 in general.
The aim of the present short note is to answer the open questions posted by Hern\'andez, Martin, and Rodrigues in {\rm \cite{p1,p2}}. The obtained results give the complete classification of irreducible components in the varieties of Jordan…
We give a complete classification of anisotropic projective homogeneous varieties of dimension less than 6 up to motivic isomorphism. We give several criteria for anisotropic flag varieties of type A_n to have isomorphic motives.
One of the fundamental questions in current field theory, related to Grothendieck's conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the…
For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields, and the…
This paper generalises Mori's famous theorem about "Projective manifolds with ample tangent bundles" to normal projective varieties in the following way: A normal projective variety over $\mathbb{C}$ with ample tangent sheaf is isomorphic…
We prove a structural result for geometrically non-reduced varieties and give applications to Fano varieties. For example, we show that if $X$ is the generic fibre of a Mori fibre space of relative dimension $n$, and the characteristic is…
We generalize Horrocks' criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension at least four, over…
The goal of this work is to study geometric properties of geometrically irreducible subschemes on degenerations of Fano varieties (more generally, of separably rationally connected varieties). It is known that these geometrically…
We give a brief overview on the theory and phenomenology of generalized parton distributions (GPDs), including the recently developed framework of single-diffractive hard exclusive process for matching GPDs to experimental observables. We…
We begin a systematic investigation of derived categories of smooth projective toric varieties defined over an arbitrary base field. We show that, in many cases, toric varieties admit full exceptional collections. Examples include all toric…