Related papers: A smooth, complete threefold with no nontrivial ne…

We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class of the even Clifford algebra…

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of…

Let $S$ be a non-uniruled (i.e., non-birationally ruled) smooth projective surface. We show that the tangent bundle $T_S$ is pseudo-effective if and only if the canonical divisor $K_S$ is nef and the second Chern class vanishes, i.e.,…

We show that some important classes of weak Fano $3$-folds of Picard rank $2$ do not satisfy Bott vanishing. Using this we show that any smooth projective $3$-fold $X$ of Picard rank $2$ with $-K_X$ nef which is the image of a projective…

We exhibit a smooth complex rational affine surface with uncountably many nonisomorphic real forms.

This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincar\'e duality…

We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.

A general theorem on the existence of natural torsion-free affine connections on a complete family of compact complex submanifolds in a complex manifold is proved. Applications to twistor theory are discussed.

Let X be a general complex Fano threefold of genus 8. We prove that the moduli space of rank two semistable sheaves on X with Chern numbers c_1=1, c_2=6 and c_3=0 is isomorphic to the Fano surface F(X) of conics on X. Inside F(X), the…

In this work are considered some questions of Monte-Carlo modeling on nontrivial bundles. As a basic example is used problem of generation of straight lines in 3D space, related with modeling of interaction of a solid body with a flux of…

We consider smooth threefolds $Y$ defined over $\Bbb{C}$ with $H^i(Y, \Omega^j_Y)=0$ for all $j\geq 0$, $i>0$. Let $X$ be a smooth projective threefold containing $Y$ and $D$ be the boundary divisor with support $X-Y$. We are interested in…

We give a new proof of the classification due to Peternell-Szurek-Wi\'{s}niewski of nef vector bundles on a projective space with the first Chern class less than three and on a smooth hyperquadric with the first Chern class less than two…

On a compact K\"ahler manifold, we introduce a notion of almost nonpositivity for the holomorphic sectional curvature, which by definition is weaker than the existence of a K\"ahler metric with semi-negative holomorphic sectional curvature.…

I prove a crystalline characterization of abelian varieties in characteristic $p>0$ amongst the class of varieties with trivial tangent bundle. I show using my characterization that a smooth, projective, ordinary variety with trivial…

Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to…

A nef-partition for a weighted complete intersection is a combinatorial structure on its weights and degrees which is important for Mirror Symmetry. It is known that nef-partitions exist for smooth well-formed Fano weighted complete…

The following results are proved: Theorem 1. A totally real semiparallel submanifold of constant curvature with parallel f-structure in the normal bundle of a K\"ahler manifold N is flat or a totally geodesic submanifold of N. Theorem 2. A…

We introduce a new technique, based on Gaussian maps, to study the possibility, for a given surface, to lie on a threefold as a very ample divisor with given normal bundle. We give several applications, among which one to surfaces of…

In this paper we give a complete description about normal monohedral tilings of a convex disc with smooth boundary where we have at most three topological discs as tiles. This result is a far-reaching generalization of the results of…

In this work we consider compact K\"ahler manifolds with non-positive mixed curvature which is a "convex combination" of Ricci curvature and holomorphic sectional curvature. We show that in this case, the canonical line bundle is nef.…