Related papers: On the Choi-Effros multiplication

We prove several extensions of the Erdos-Fuchs theorem.

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.

We give a short proof for the Hartogs's extension theorem on (n-1)-complete complex spaces.

A short proof of the elliptical range theorem concerning the numerical range of $2\times2$ complex matrices is given.

We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

We proove a Bloch's theorem in an almost complex projective plane.

We give a new proof of the Adams-Riemann-Roch theorem for a smooth projective morphism $X\to Y$, in the situation where $Y$ is a regular scheme, which is quasi-projective over $\mF_p$. We also partially answer a question of B. K\"ock.

Using an alternative notion of good reduction, an analog of the Shafarevich theorem for elliptic curves is proved for morphisms of the projective line over number fields.

This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.

A short and almost elementary proof of the Boros-F\"uredi-B\'ar\'any-Pach-Gromov theorem on the multiplicity of covering by simplices in $\mathbb R^d$ is given.

For a certain class of configurations of points in space, Eves' Theorem gives a ratio of products of distances that is invariant under projective transformations, generalizing the cross-ratio for four points on a line. We give a…

We give a short, elementary and explicit proof of the existence of Hilbert schemes of points on affine schemes. As a direct consequence we obtain the existence of the Hilbert scheme of points on any projective scheme, not necessarily of…

This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the…

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…

We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

We prove several formulas for the distribution of positive roots.

We prove finite-field analogs of Bourgain's projection theorem in higher dimensions. In particular, for a certain range of parameters we improve on an exceptional set estimate by Chen in all dimensions and codimensions.

In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.