Related papers: Strictly nef Bundles

Let $X$ be the wonderful compactification of a complex symmetric space $G/H$ of minimal rank. For a point $x\,\in\, G$, denote by $Z$ be the closure of $BxH/H$ in $X$, where $B$ is a Borel subgroup of $G$. The universal cover of $G$ is…

Let $X$ be a normal, connected and projective variety over an algebraically closed field $k$. It is known that a vector bundle $V$ on $X$ is essentially finite if and only if it is trivialized by a proper surjective morphism $f:Y\to X$. In…

Let $X$ be a normal projective variety equipped with an action of a semisimple algebraic group $G$, and assume that $X$ contains a unique closed orbit. Let $B$ be a Borel subgroup of $G$ and let $E$ be a $B$-equivariant vector bundle on…

We show that a nef line bundle on a proper scheme over an excellent base is semiample if and only if it is semiample after restricting to characteristic zero and to positive characteristic. In the process of the proof, we provide a…

In this paper, we study when positivity conditions of vector bundles are preserved by extension. We prove that an extension of a big (resp. pseudo-effective) line bundle by an ample (resp. a nef) vector bundle is big (resp.…

Let X be a smooth complex projective curve of genus g bigger or equal to 1. If g is bigger than 1 assume further that X is either bielliptic or with general moduli. Under a natural condition on slopes, we prove that there exists a short…

We study the problem of when a topological vector bundle on a smooth complex affine variety admits an algebraic structure. We prove that all rank $2$ topological complex vector bundles on smooth affine quadrics of dimension $11$ over the…

Let $X$ be a smooth projective variety over the complex numbers. One knows by the Cone Theorem that the closed cone of curves of $X$ is rational polyhedral whenever $c_1(X)$ is ample. For varieties $X$ such that $c_1(X)$ is not ample,…

We show that the tangent bundle of a projective manifold with nef anticanonical class is generically nef. That is, its restriction to a curve cut out by general sufficiently ample divisors is a nef vector bundle. This confirms a conjecture…

Serrrano's Conjecture says that if $L$ is a strictly nef line bundle on a smooth projective variety $X$, then $K_X+tL$ is ample for $ t > dim X+1$. In this paper I will prove a few cases of this conjecture. I will also prove a generalized…

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an…

The cotangent bundle of a non-uniruled projective manifold is generically nef, due to a theorem of Miyaoka. We show that the cotangent bundle is actually generically ample, if the manifold is of general type and study in detail the case of…

In this note we show that every (real or complex) vector bundle over a compact rank one symmetric space carries, after taking the Whitney sum with a trivial bundle of sufficiently large rank, a metric with nonnegative sectional curvature.…

A $k$-very ample line bundle L on a Del Pezzo Surface is numerically characterized. We find that the set of the exceptional curves and effective divisors with selfintersection zero, $\cal S$, plays a very important rule in checking the…

We classify nef vector bundles on a smooth hyperquadric of dimension $\geq 4$ with first Chern class two over an algebraically closed field of characteristic zero.

We prove that a smooth complex projective threefold with a K\"ahler metric of negative holomorphic sectional curvature has ample canonical line bundle. In dimensions greater than three, we prove that, under equal assumptions, the nef…

Let $X$ be a compact complex manifold of dimension $n\ge 2$ and $\ce$ an ample vector bundle of rank $r<n$ on $X$. As the continuation of Part I, we further study the properties of $g(X,\ce)$ that is an invariant for pairs $(X,\ce)$ and is…

We prove that if a curve of a non-isotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety then it is special.

We present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety $V$ in terms of the geometric degree of $V$. We first analyze the case of curves, showing an explicit relation…

We explain how to define an embedding of a tame stack over a noetherian ring into a certain generalization of a weighted projective stack using a notion of ample vector bundle on the stack. As applications we construct algebraic moduli…