Manis valuations and Prüfer extensions. I.
Matching local Witt invariants
The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence — once it is expressed in terms of the Witt invariant — admits a natural generalisation. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.
Moduli spaces of stable real algebraic curves
Multivariate moment problems : geometry and indeterminateness
The most accurate determinateness criteria for the multivariate moment problem require the density of polynomials in a weighted Lebesgue space of a generic representing measure. We propose a relaxation of such a criterion to the approximation of a single function, and based on this condition we analyze the impact of the geometry of the support on the uniqueness of the representing measure. In particular we show that a multivariate moment sequence is determinate if its support has dimension one and...
Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods
We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces...