Related papers: A Matsusaka-type Theorem for Surfaces
Generalizations of the classical affine Lelieuvre formula to surfaces in projective three-dimensional space and to hypersurfaces in multi- dimensional projective space are given. A discrete version of the projective Lelieuvre formula is…
In this paper we present a Kakutani type theorem that is equivalent to the Borsuk--Ulam theorem for manifolds.
We prove an effective bound for the degree of a smooth divisor of a hypersurface of P^n, n>4 (projective space over an algebraically closed field of characteristic zero). Our result follows from a strong (since the degree of the divisor is…
Motivated by the recent surge of interest in the geometry of hybrid spaces, we prove an Abel-Jacobi theorem for a metrized complex of Riemann surfaces, generalizing both the classical Abel-Jacobi theorem and its tropical analogue.
My main results are simple formulas for the surface area of d-dimensional lattice polytopes using Ehrhart theory.
We prove that a smooth surface, non of general type, in projective four-space, which lies on a quartic hypersurface with isolated singularities has degree at most 27 (in fact we prove a slightly more general result).
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.
In this paper, we will first prove a Liouville theorem to a torsion system. As an application, complete resolutions of symmetry group to the porous medium equation of Fujita type are obtained for symmetric spaces.
The issue and proof of Gurzadyan theorem are presented concisely, avoiding tedious and unnecessary calculations that would mask what is essential. The goal is to provide a good mathematical and physical understanding of the theorem, making…
In this paper, we prove a version of the arithmetic Bertini theorem asserting that there exists a strictly small and generically smooth section of a given arithmetically free graded arithmetic linear series.
In this note we fill a gap in the proof of the main theorem (Theorem 1.2) of our paper 'Surfaces in 4-manifolds', Math. Res. Letters 4 (1997), 907-914.
We prove a theorem on the existence of global surfaces of section with prescribed spanning orbits and homology class. This result is a modification and a refinement of a result due to Fried, recast in terms of invariant measures instead of…
The procedure for constructing the massive particle surfaces in static space-times is described in detail and the equivalence of the main results with the results of the geodesic approach is demonstrated.
Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…
In this note we consider a question related to the high-dimensional generalization of the classical Severi's finiteness theorem for curves. We will introduce some background and then state the main result. The proof of the main result is…
We show that using an idea from a paper by Van de Ven one may obtain a simple proof of Zak's classification of smooth projective surfaces with zero vanishing cycles. This method of proof allows one to extend Zak's theorem to the case of…
A theorem of Jannsen asserts that if a smooth projective variety has injective cycle class maps, it has surjective cycle class maps. The object of this note is to present a version of Jannsen's theorem for singular quasi--projective…
Let M be a Q-divisor on a smooth surface over C. In this paper we give criteria for very ampleness of the adjoint of the round-up of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of…
This article derives closed-form parametric formulas for the Minkowski sums of convex bodies in d-dimensional Euclidean space with boundaries that are smooth and have all positive sectional curvatures at every point. Under these conditions,…
From radial curvature geometry's standpoint, we prove a sphere theorem of the Grove-Shiohama type for a certain class of compact Finsler manifolds.