Related papers: Projective generalizations of Lelieuvre's formula
For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs…
A theorem of Wiegerinck asserts that the Bergman space of an open subset of the complex numbers is either infinite-dimensional or trivial. Recently, this has been generalized to holomorphic vector bundles over the projective line by the…
We take points and planes as fundamental, lines as derived, in an axiomatic formulation of three-dimensional projective space, the self-dual nature of which formulation renders automatic the principle of duality.
Some generalizations of the classical Hurewicz formula are obtained for extension dimension and C-spaces.
Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.
We show how Seifert surfaces, so useful for the understanding of the Alexander polynomial \Delta_L(t), can be generalized in order to study the multivariable Alexander polynomial \Delta_L(t_1,...,t_\mu). In particular, we give an elementary…
The geometric Tevelev degrees of projective space enumerate general, pointed algebraic curves interpolating through the maximal possible number of points. Previous work expresses these invariants in terms of Schubert calculus. Extending…
A formula for the irregularity of abelian coverings of the projective plane is established and some applications are presented.
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
In this short note, we investigate the generalization of Lehmer's problem to finitely generated fields over $\mathbb{Q}$.
Many product formulas are known classically for generalized hypergeometric functions over the complex numbers. In this paper, we establish some analogous formulas for generalized hypergeometric functions over finite fields.
In this article we will construct the Liouville parametrization of the triaxial ellipsoid. In the literature quadrics are given as examples of Liouville surfaces, yet no one gives such a parametrization. For this we introduce the…
We study complements of hypersurfaces in schemes with respect to the property being affine.
We prove sharp $L^2$ Fourier restriction inequalities for compact, smooth surfaces in $\mathbb{R}^3$ equipped with the affine surface measure or a power thereof. The results are valid for all smooth surfaces and the bounds are uniform for…
In this paper, we consider the orthogonal projection of a surface in $\mathbb{R}^3$ for a given view direction. We then introduce and investigate several invariants of the families of the plane curves that locally configure the projection…
We extend a result of to Esnault-Levine-Viehweg concerning the Chow groups of hypersurfaces in projective space to those in weighted projective spaces.
In this note we find a generic defining function of projective motion in the 6-dimensional rigid h-space.
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
The Hilbert scheme of projective 3-folds of codimension 3 or more that are linear scrolls over the projective plane or over a smooth quadric surface or that are quadric or cubic fibrations over the projective line is studied. All known such…
We extend the notion of illumination bodies to Riemannian spaces of constant curvature and to projective Finsler geometries. We prove that the derivative of their volume defines a notion of surface area for convex bodies in these settings,…