Andradas Heranz, Carlos y Ruiz Sancho, Jesús María (1994) Low dimensional sections of basic semialgebraic sets. Illinois Journal of Mathematical, 38 (2). pp. 303-326. ISSN 0019-2082
Restringido a Sólo personal autorizado del repositorio hasta 2020.
URL Oficial: http://projecteuclid.org/handle/euclid.ijm
Let X be a real affine algebraic set and S a semialgebraic set. Many important results are known about the basicness of S: mainly, if S is basic open, S can be defined by s strict inequalities, where s is bounded by the dimension of X. It is also known (Br¨ocker-Scheiderer criterion) that
an open semialgebraic set is basic and is defined by s inequalities (s-basic) if and only if for every irreducible subset Y of X the intersection S \ Y is generically s-basic. In a previous paper, the authors proved that to test the basicness of S it is sufficient to test the basicness of the intersections of S with every irreducible surface. In fact, this is the best possible result about the dimension, but it was conjectured by the authors that the first obstruction to s-basicness should be recognized in
In the present paper, the authors confirm this conjecture, and in fact they prove the following result: if S is basic, then S is s-basic if and only if for every irreducible subset Y ofX of dimension s+1 the intersection S \Y is generically s-basic.
The proof of this theorem requires a deep analysis of real valuations. The results of independent interest about fans (algebroid fans) defined by means of power series and the approximation problem solved in this case are the main tools of the proof.
|Tipo de documento:||Artículo|
|Palabras clave:||basic open semi-algebraic set; fans; real spectrum|
|Materias:||Ciencias > Matemáticas > Geometria algebraica|
|Depositado:||18 Abr 2012 08:47|
|Última Modificación:||06 Feb 2014 10:09|
Descargas en el último año
Sólo personal del repositorio: página de control del artículo