Real Algebraic Geometry and Ordered Structures

by AMS Special Session on Real Algebraic Geometry; Delzell, Charles N.; Madden, James J.

• ISBN13: 9780821808047
• ISBN10: 0821808044
• Format: Paperback
• Copyright: 2000-03-01
• Publisher: Amer Mathematical Society

Summary

This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.

Table of Contents

Preface	ix
On real involutions and ramifications of real valuations	1	(18)
M. E. Alonso
M. P. Velez
Deciding positivity of real polynomials	19	(6)
Eberhard Becker
Victoria Powers
Thorsten Wormann
Radial vector fields and the Poincare-Hopf theorem	25	(6)
Jean-Paul Brasselet
A generalization of the Arnold-Viro inequalities for real singular algebraic curves	31	(8)
Sergey Finashin
Floppy curves, with applications to real algebraic curves	39	(38)
Patrick Gilmer
Towards as abstract description of the space of real places	77	(38)
Danielle Gondard
Murray Marshall
A special quantifier elimination algorithm for Pham systems	115	(20)
Laureano Gonzalez-Vega
A look at biseparating maps from an algebraic point of view	135	(10)
Melvin Henriksen
Frank A. Smith
Real Teichmuller spaces and moduli of real algebraic curves	145	(34)
J. Huisman
Correction to ``A real algebraic vector bundle is strongly algebraic whenever its total space is affine''	179	(2)
J. Huisman
The exponential rank of nonarchimedean exponential fields	181	(22)
Franz-Viktor Kuhlmann
Salma Kuhlmann
Subanalytic and semialgebraic realisations of abstract stratified sets	203	(6)
Laurent Noirel
David Trotman
On the vector space defect for valued field extensions	209	(10)
Jack Ohm
On the classification of decomposable 7-th degree curves	219	(16)
Grigorii M. Polotovskii
The complex spectrum of a ring	235	(16)
M. J. de la Puente
Some concrete aspects of Hilbert's 17th problem	251	(22)
Bruce Reznick
Semialgebraic singularity theory	273
Masahiro Shiota