Related papers: Algebraic varieties with quasi-projective universa…

In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we…

We prove some results on effective very ampleness and projective normality for some varieties with trivial canonical bundle. In the first part we prove an effective projective normality result for an ample line bundle on regular smooth…

We give evidence for a uniformization-type conjecture, that any algebraic variety can be altered into a variety endowed with a tower of smooth fibrations of relative dimension one.

We characterise the virtually abelian groups which are fundamental groups of compact K\"ahler manifolds and of smooth projective varieties. We show that a virtually abelian group is K\"ahler if and only if it is projective. In particular,…

A vector bundle E on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. A theorem of Nori implies that E is finite if and only if the pullback of E to some finite etale…

Let $X$ be a smooth projective variety defined over an algebraically closed field of positive characteristic $p$ whose tangent bundle is nef. We prove that $X$ admits a smooth morphism $X \to M$ such that the fibers are Fano varieties with…

We show that there exists no smooth fibration of a smooth complex quasi-projective variety of log-general type over a quasi-abelian variety. The proof uses M. Popa and C. Schnell's construction of Higgs bundle.

We extend the usual projective Abel-Radon transform to the larger context of a smooth complete toric variety X. We define and study toric concavity attached to an algebraic splitting vector bundle on X and we prove a toric version of the…

We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample…

We prove an elementary but somewhat unexpected result about projective embeddings of smooth varieties X whose cotangent bundles are numerically effective. Specifically, we show that the degree of X in any projective embedding must grow…

Every fibration of a projective hyper-K\"ahler fourfold has fibers which are Abelian surfaces. In case the Abelian surface is a Jacobian of a genus two curve, these have been classified by Markushevich. We study those cases where the…

We introduce the notion of a projectively simple ring, which is an infinite-dimensional graded k-algebra A such that every 2-sided ideal has finite codimension in A (over the base field k). Under some (relatively mild) additional…

Let G be a semisimple connected linear algebraic group over C, and X a wonderful G-variety. We study the possibility of realizing X as a closed subvariety of the projective space of a simple G-module. We describe the wonderful varieties…

We define partially ample subvarieties of projective varieties, generalizing Ottem's work on ample subvarieties, and show their ubiquity. As an application, we obtain a connectedness result for pre-images of subvarieties by morphisms,…

We consider all complex projective manifolds X that satisfy at least one of the following three conditions: 1. There exists a pair $(C ,\varphi)$, where $C$ is a compact connected Riemann surface and $\varphi : C\to X$ a holomorphic map,…

Sommese has conjectured a classification of smooth projective varieties X containing, as an ample divisor, a P^d-bundle Y over a smooth variety Z. This conjecture is known if d>1, if dim(X)<5, or if Z admits a finite morphism to an Abelian…

We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivity of orbifold groups. We also prove a structure theorem for…

Motivated by the theory of Inoue-type varieties, we give a structure theorem for projective manifolds $W_0$ with the property of admitting a 1-parameter deformation where $W_t$ is a hypersurface in a projective smooth manifold $Z_t$. Their…

We show that an abelian surface embedded in P^N by a very ample line bundle L of type (1,2d) is projectively normal if and only if d>=4. This completes the study of the projective normality of abelian surfaces embedded by complete linear…

For an ordinary abelian variety $X$, $F^e_*\mathcal{O}_X$ is decomposed into line bundles for every positive integer $e$. Conversely, if a smooth projective variety $X$ satisfies this property and its Kodaira dimension is non-negative, then…