# Real Algebraic Geometry and Ordered Structures

Share this page *Edited by *
*Charles N. Delzell; James J. Madden*

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.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry.

# Table of Contents

## Real Algebraic Geometry and Ordered Structures

- Contents vii8 free
- Preface ix10 free
- On real involutions and ramifications of real valuations 130 free
- Deciding positivity of real polynomials 1948
- Radial vector fields and the Poincaré-Hopf theorem 2554
- A generalization of the Arnold-Viro inequalities for real singular algebraic curves 3160
- Floppy curves, with applications to real algebraic curves 3968
- Towards an abstract description of the space of real places 77106
- A special quantifier elimination algorithm for Pham systems 115144
- A look at biseparating maps from an algebraic point of view 135164
- Real Teichmüller spaces and moduli of real algebraic curves 145174
- 1. Introduction 146175
- 2. Complex algebraic curves and Riemann surfaces 149178
- 3. Antialgebraic and antiholomorphic actions 150179
- 4. Real algebraic curves and Riemann surfaces 151180
- 5. Topology of real algebraic curves 152181
- 6. Complex structures 156185
- 7. Conformal structures 157186
- 8. Complex and conformal structures 157186
- 9. Beltrami coefficients 159188
- 10. Complex dilation 160189
- 11. Almost complex manifolds 160189
- 12. Complex analytic and almost complex manifolds 161190
- 13. Conformal manifolds 162191
- 14. Almost complex and conformal manifolds 162191
- 15. Realizing a topological type 163192
- 16. Connectedness of moduli spaces by elementary techniques 164193
- 17. Beltrami differentials 165194
- 18. Quasiconformal homeomorphisms 167196
- 19. Complex Teichmiiller spaces 168197
- 20. Real Teichmüller spaces 170199
- 21. Teichmüller's Theorem 172201
- 22. Moduli of real algebraic curves 174203
- References 176205

- Correction to "A real algebraic vector bundle is strongly algebraicwhenever its total space is affine" 179208
- The exponential rank of nonarchimedean exponential fields 181210
- Subanalytic and semialgebraic realisations of abstract stratified sets 203232
- On the vector space defect for valued field extensions 209238
- On the classification of decomposable 7-th degree curves 219248
- The complex spectrum of a ring 235264
- Some concrete aspects of Hilbert's 17th problem 251280
- Semialgebraic singularity theory 273302