Related papers: Four Points and a Quadric

We prove an analog of Lagrange's Theorem for continued fractions on the Heisenberg group: points with an eventually periodic continued fraction expansion are those that satisfy a particular type of quadratic form, and vice-versa.

Hesse claimed that an irreducible projective hypersurface in $\PP^n$ defined by an equation with vanishing hessian determinant is necessarily a cone. Gordan and Noether proved that this is true for $n\leq 3$ and constructed counterexamples…

New results on comparison of distributions of Gaussian quadratic forms are presented

The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…

A very simple but useful almost sure convergence theorem of probability is given.

We present in this work a new and simple proof of the false centre theorem.

In this note we shall give a new proof to a quadrature formulae due to Newton.

This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.

In this article, we prove a theorem comparing the dihedral angles of simplices in the hyperbolic, spherical and Euclidean geometries.

We show that the hessian map of quartic plane curves is a birational morphism onto its image, thus bringing new evidence for a very interesting conjecture of Ciro Ciliberto and Giorgio Ottaviani. Our new approach also yields a simpler proof…

We prove the following result which was conjectured by Stichtenoth and Xing: let $g$ be the genus of a projective, irreducible non-singular curve over the finite field $\Bbb F_{q^2}$ and whose number of $\Bbb F_{q^2}$-rational points…

We establish a torsion theorem to the effect that the unique zero of the Kodaira-Spencer map attached to a certain quasi-semistable family of complex projective varieties over the complex projective line is the image of a torsion point of…

In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…

We extend to any dimension the quantitative fourth moment theorem on the Poisson setting, recently proved by C. D\"obler and G. Peccati (2017). In particular, by adapting the exchangeable pairs couplings construction introduced by I.…

The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.

This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasi-homogeneous…

We prove that the Hilbert scheme of points on a normal quasi-projective surface with at worst rational double point singularities is irreducible.

The classical version of B\'ezout's Theorem gives an integer-valued count of the intersection points of hypersurfaces in projective space over an algebraically closed field. Using work of Kass and Wickelgren, we prove a version of…

We give an elementary proof of a recent result by Fishman, Kleinbock, Merrill and Simmons about rational points on quadratic surfaces.

Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…