Real Algebraic Geometry and Ordered Structures / Edition 1

Real Algebraic Geometry and Ordered Structures / Edition 1

by Charles N. Delzell
     
 

This volume contains 16 carefully refereed articles by participants in the Special Session on Real Algebraic Geometry and Ordered Algebraic Structures at the Sectional Meeting of the AMS in Baton Rouge, April 1996, and the associated Special Semester in the spring of 1996 at Louisiana State University and Southern University, Baton Rouge. The 23 contributors to

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Overview

This volume contains 16 carefully refereed articles by participants in the Special Session on Real Algebraic Geometry and Ordered Algebraic Structures at the Sectional Meeting of the AMS in Baton Rouge, April 1996, and the associated Special Semester in the spring of 1996 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. 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.

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Product Details

ISBN-13:
9780821808047
Publisher:
American Mathematical Society
Publication date:
03/01/2000
Series:
Contemporary Mathematics Series, #253
Pages:
287
Product dimensions:
7.09(w) x 9.84(h) x (d)

Related Subjects

Table of Contents

Prefaceix
On real involutions and ramifications of real valuations1
Deciding positivity of real polynomials19
Radial vector fields and the Poincare-Hopf theorem25
A generalization of the Arnold-Viro inequalities for real singular algebraic curves31
Floppy curves, with applications to real algebraic curves39
Towards an abstract description of the space of real places77
A special quantifier elimination algorithm for Pham systems115
A look at biseparating maps from an algebraic point of view135
Real Teichmuller spaces and moduli of real algebraic curves145
Correction to "A real algebraic vector bundle is strongly algebraic whenever its total space is affine"179
The exponential rank of nonarchimedean exponential fields181
Subanalytic and semialgebraic realisations of abstract stratified sets203
On the vector space defect for valued field extensions209
On the classification of decomposable 7-th degree curves219
The complex spectrum of a ring235
Some concrete aspects of Hilbert's 17th problem251
Semialgebraic singularity theory273

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