Real Algebraic Geometry and Ordered Structures.

Intro -- Contents -- Preface -- On real involutions and ramifications of real valuations -- Deciding positivity of real polynomials -- Radial vector fields and the Poincaré-Hopf theorem -- A generalization of the Arnold-Viro inequalities for real singular algebraic curves -- Floppy curves, with applications to real algebraic curves -- Towards an abstract description of the space of real places -- A special quantifier elimination algorithm for Pham systems -- A look at biseparating maps from an algebraic point of view -- Real Teichmüller spaces and moduli of real algebraic curves -- 1. Introduction -- 2. Complex algebraic curves and Riemann surfaces -- 3. Antialgebraic and antiholomorphic actions -- 4. Real algebraic curves and Riemann surfaces -- 5. Topology of real algebraic curves -- 6. Complex structures -- 7. Conformal structures -- 8. Complex and conformal structures -- 9. Beltrami coefficients -- 10. Complex dilation -- 11. Almost complex manifolds -- 12. Complex analytic and almost complex manifolds -- 13. Conformal manifolds -- 14. Almost complex and conformal manifolds -- 15. Realizing a topological type -- 16. Connectedness of moduli spaces by elementary techniques -- 17. Beltrami differentials -- 18. Quasiconformal homeomorphisms -- 19. Complex Teichmiiller spaces -- 20. Real Teichmüller spaces -- 21. Teichmüller's Theorem -- 22. Moduli of real algebraic curves -- References -- Correction to "A real algebraic vector bundle is strongly algebraicwhenever its total space is affine -- The exponential rank of nonarchimedean exponential fields -- Subanalytic and semialgebraic realisations of abstract stratified sets -- On the vector space defect for valued field extensions -- On the classification of decomposable 7-th degree curves -- The complex spectrum of a ring -- Some concrete aspects of Hilbert's 17th problem.

Semialgebraic singularity theory.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.