Real Algebraic Geometry and Ordered Structures
About this Title
Charles N. Delzell and James J. Madden, Editors
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.
Graduate students and research mathematicians interested in algebraic geometry.
Table of Contents
- M. E. Alonso and M. P. Vélez – On real involutions and ramification of real valuations [MR 1747574]
- Eberhard Becker, Victoria Powers and Thorsten Wörmann – Deciding positivity of real polynomials [MR 1747575]
- Jean-Paul Brasselet – Radial vector fields and the Poincaré-Hopf theorem [MR 1747576]
- Sergey Finashin – A generalization of the Arnold-Viro inequalities for real singular algebraic curves [MR 1747577]
- Patrick M. Gilmer – Floppy curves, with applications to real algebraic curves [MR 1747578]
- Danielle Gondard and Murray Marshall – Towards an abstract description of the space of real places [MR 1747579]
- Laureano Gonzalez-Vega – A special quantifier elimination algorithm for Pham systems [MR 1747580]
- M. Henriksen and F. A. Smith – A look at biseparating maps from an algebraic point of view [MR 1747581]
- J. Huisman – Real Teichmüller spaces and moduli of real algebraic curves [MR 1747582]
- J. Huisman – Correction to: “A real algebraic vector bundle is strongly algebraic whenever its total space is affine” [in Real algebraic geometry and topology (East Lansing, MI, 1993), 117–119, Contemp. Math., 182, Amer. Math. Soc., Providence, RI, 1995; MR1318734 (95m:14036)] [MR 1747583]
- Franz-Viktor Kuhlmann and Salma Kuhlmann – The exponential rank of nonarchimedean exponential fields [MR 1747584]
- Laurent Noirel and David Trotman – Subanalytic and semialgebraic realisations of abstract stratified sets [MR 1747585]
- Jack Ohm – On the vector space defect for valued field extensions [MR 1747586]
- Grigorii M. Polotovskii – On the classification of decomposable 7-th degree curves [MR 1747587]
- M. J. de la Puente – The complex spectrum of a ring [MR 1747588]
- Bruce Reznick – Some concrete aspects of Hilbert’s 17th Problem [MR 1747589]
- Masahiro Shiota – Semialgebraic singularity theory [MR 1747590]