Related papers: Rational connectedness for groups of proper projec…

In this paper, we consider {\em mixed curvature} $\mathcal{C}_{a,b}$, which is a convex combination of Ricci curvature and holomorphic sectional curvature introduced by Chu-Lee-Tam. We prove that if a compact complex manifold $M$ admits a…

T. Kambayashi had shown that $\mathbb{A}^2$-forms over separable field extensions are necessarily polynomial rings. However, there exist inseparable $\mathbb{A}^2$-forms which are not necessarily polynomial rings. In this paper, we give a…

Let X be a normal projective variety of dimension n > 2 admitting the action of the group G := Z^{n-1} such that every non-trivial element of G is of positive entropy. We show: `X is not rationally connected' ==> `X is G-equivariant…

Recently, the rings whose injective right modules are R-projective (respectively, max-projective) were investigated and studied in [2]. Such ring are called right almost-QF (respectively, max-QF). In this paper, our aim is to give some…

This article proves hypersurfaces of degree d in projective n-space are "rationally simply-connected" if $d^2 \leq n$. In a forthcoming paper, de Jong and I prove a slightly weaker result when $d^2 \leq n+1$.

Generalizing a theorem of Springer, we construct an extended Arason filtration by subgroups for the Witt group of quadratic forms of a general valued field, relating these subgroups with Witt-like groups of the residue field, in arbitrary…

Planar systems with a general linear spin-orbit interaction (SOI) that can be cast in the form of a non-Abelian pure gauge field are investigated using the language of non-Abelian gauge field theory. A special class of these fields that,…

System of alternatively orthogonalized rational functions of Jacobi type on the half line $[1, \infty)$ is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties…

Let $\mathfrak{R}$ and $\mathfrak{R}'$ be two associative rings (not necessarily with the identity elements). A bijective map $\varphi$ of $\mathfrak{R}$ onto $\mathfrak{R}'$ is called a \textit{$m$-multiplicative isomorphism} if {$\varphi…

In the present paper, we prove the retract rationality of the classifying spaces $BG$ for several types of finite connected group schemes $G$ over algebraically closed fields of positive characteristic $p>0$. In particular, we prove the…

This paper investigates the relationship between the hyperbolicity of complex quasi-projective varieties $X$ and the (topological) fundamental group $\pi_1(X)$ in the presence of a linear representation $\varrho: \pi_1(X) \to {\rm…

Let X be a projective cubic hypersurface of dimension 11 or more, which is defined over the rationals. In this paper it is shown that X contains rational points provided that the cubic form defining X can be written as the sum of two forms…

We give a short constructive proof for the existence and uniqueness of the rational normal form of a quadratic matrix.

For each positive prime integer $p$ we construct a standard graded $F$-rational ring $R$, over a field $K$ of characteristic $p$, such that $R\otimes_K\overline{K}$ is not $F$-rational. By localizing we obtain a flat local homomorphism $(R,…

Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration with rationally connected fibers. We apply…

For a normal projective variety $X$, the $\bf Q$-factoriality defect $\sigma(X)$ is defined to be the rank of the quotient of the group of Weil divisors by the subgroup of Cartier ones. We prove a slight improvement of a topological formula…

We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…

The family of varieties of minimal rational tangents on a quasi-homogeneous projective manifold is isotrivial. Conversely, are projective manifolds with isotrivial varieties of minimal rational tangents quasi-homogenous? We will show that…

We generalize to arbitrary dimension our previous construction of simply connected weakly-special but not special varieties. We show that they satisfy the function field and complex analytic part of Campana's conjecture. Moreover, we give…

For a field $E$ of characteristic different from $2$ and cohomological $2$-dimension one, quadratic forms over the rational function field $E(X)$ are studied. A characterisation in terms of polynomials in $E[X]$ is obtained for having that…