Orthogonal pairings of Euclidean spaces.

Tautological Pairings on Moduli Spaces of Curves

We discuss analogs of Faber’s conjecture for two nested sequences of partial compactifications of the moduli space of smooth curves. We show that their tautological rings are one-dimensional in top degree but do not satisfy Poincaré duality. The structure of the tautological ring of the moduli space of stable curves is predicted by the Faber conjecture, which states that R(Mg,n) is Gorenstein w...

A Characterization of Euclidean Spaces

The purpose of this paper is to give an elementary proof of the fact that a Banach space in which there exist projection transformations of norm one on every two-dimensional linear subspace is a euclidean space. S. Kakutani [ l ] has pointed out that a modification of a proof due to Blaschke [2] will prove this theorem. F. Bohnenblust has been able to establish this theorem for the complex case...

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

On Isometries of Euclidean Spaces

Berkovich Spaces Embed in Euclidean Spaces

Let K be a eld that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analyti cation V an of any d-dimensional quasi-projective scheme V over K embeds in R. If, moreover, the value group of K is dense in R>0 and V is a curve, then we describe the homeomorphism type of V an by using the theory of local dendrites.