Related papers: A remark on hyperplane sections of rational normal…

A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…

We show that a divisor in a rational homogenous variety with split normal sequence is the preimage of a hyperplane section in either the projective space or a quadric.

The classification of projective elliptic line scrolls with the description of their singular loci is given. In particular we recover Atiyah Theorem by using classical methods.

This paper presents a few remarks about the topology of symplectic hyperplane sections and the geometry of their complements. In particular, it contains a detailed proof of the following result already stated with hints in [Gi]: for…

We present the topological classification of real parts of real regular elliptic surfaces with a real section.

This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the…

It is known that the smooth rational threefolds of P^5 having a rational non-special surface of P^4 as general hyperplane section have degree d=3,... ,7. We study such threefolds X from the point of view of linear systems of surfaces in…

This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…

We define natural classes of rational and polynomial representations of the Yangian of the general linear Lie algebra. We also present the classification and explicit realizations of all irreducible rational representations of the Yangian.

The purpose of this paper is to explain a method on the generalization of the Bertini-type theorem on standard graded rings to the non-standard graded case of certain type.

We prove analogues of several well-known results concerning rational morphisms between quadrics for the class of so-called quasilinear $p$-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric…

A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points in the plane. We display a one-to-one correspondence between…

Fix positive integers $n,r,d$. We show that if $n,r,d$ satisfy a suitable inequality, then any smooth hypersurface $X\subset \mathbb{P}^n$ defined over a finite field of characteristic $p$ sufficiently large contains a rational $r$-plane.…

We prove that the Euler-Chow series for ruled surfaces and scrolls is rational by means of an explicit computation.

We study families of scrolls containing a given rational curve and families of rational curves contained in a fixed scroll via a stratification in terms of the degree of the induced map onto P^1 and we prove that there is no rational normal…

We describe a new method for constructing a spectrahedral representation of the hyperbolicity region of a hyperbolic curve in the real projective plane. As a consequence, we show that if the curve is smooth and defined over the rational…

This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…

We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.

We introduce a class of graphs with coloured edges to encode subsystems of the classical root systems, which in particular classify them up to equivalence. We further use the graphs to describe root-kernel intersections, as well as…

We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.