Related papers: Characterizing Projective Spaces for Varieties wit…

We prove a numerical characterization of $\mathbb{P}^n$ for varieties with at worst isolated local complete intersection quotient singularities. In dimension three, we prove such a numerical characterization of $\mathbb{P}^3$ for normal…

In this paper we give a short and elementary proof of a characterization of the projective space in terms of rational curves which was conjectured by Mori and Mukai. A proof was first given in a preprint by K. Cho, Y. Miyaoka and N.…

Ball quotients, hyperelliptic varieties, and projective spaces are characterized by their Chern classes, as the varieties where the Miyaoka-Yau inequality becomes an equality. Ball quotients, Abelian varieties, and projective spaces are…

We consider characterizations of projective varieties in terms of their tangents. S. Mori established the characterization of projective spaces in arbitrary characteristic by ampleness of tangent bundles. J. Wahl characterized projective…

We study projective varieties $X \subset \mathbb{P}^r$ of dimension $n \geq 2$, of codimension $c \geq 3$ and of degree $d \geq c + 3$ that are of maximal sectional regularity, i.e. varieties for which the Castelnuovo-Mumford regularity…

We define a quasi--projective reduction of a complex algebraic variety $X$ to be a regular map from $X$ to a quasi--projective variety that is universal with respect to regular maps from $X$ to quasi--projective varieties. A toric…

Projective structures on compact real manifolds are classical objects in real differential geometry. Complex manifolds with a holomorphic projective structure on the other hand form a special class as soon as the dimension is greater than…

We prove that a smooth projective variety of dimension n is isomorphic to projective n-space iff the canonical class is -(n+1)-times an ample divisor. In characteristic zero this was proved by Kobayashi-Ochiai. We also extend the second…

We study degenerations of complex projective spaces $\mathbb P^n$ into normal projective klt varieties $X$. If the tangent sheaf of $X$ is semi-stable, we show that $X$ itself is a projective space. If $X$ is a threefold with canonical…

In this paper we improve the known bound for the $X$-rank $R_{X}(P)$ of an element $P\in {\mathbb{P}}^N$ in the case in which $X\subset {\mathbb P}^n$ is a projective variety obtained as a linear projection from a general $v$-dimensional…

Let $X$ be a smooth complex projective variety. A recent conjecture of S. Kov\'acs states that if t\ he $p^{\text{th}}$-exterior power of the tangent bundle $T_X$ contains the $p^{\text{th}}$-exterior power of an ample vector bundle, then…

We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and…

Let $X$ be a four-dimensional projective variety defined over the field of complex numbers with only terminal singularities. We prove that if the intersection number of the canonical divisor $K$ with every very general curve is positive…

In this article we give a necessary and sufficient condition to characterize projective submanifolds in ${\mathbb P}^N$ with codimensions 2 and 3. The conditions involve the Chern classes of the manifold and a very ample line bundle on the…

We show that the normal points of a cubic hypersurface in projective space have canonical singularities unless the hypersurface is an iterated cone over an elliptic curve. As an application, we give a simple linear algebraic description of…

It is known that Chern characteristic numbers of compact complex manifolds cannot have arbitrary values. They satisfy certain divisability conditions. W. Ebeling and S. M. Gusein-Zade gave a definition of Chern characteristic numbers of…

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…

We prove Kov\'acs' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective…

Given integers r>1, n>1 and q> n-2, we consider projective varieties X of dimension r+1 such that through n generic points of X passes a rational curve of degree q, contained in X. More precisely, we study the class X_{r+1,n}(q) of such…

A $\mathbf{Q}$-Cartier divisor $D$ on a projective variety $M$ is {\it almost nup}, if $(D , C) > 0$ for every very general curve $C$ on $M$. An algebraic variety $X$ is of {\it almost general type}, if there exists a projective variety $M$…