Real Algebraic Geometry: Proceedings of the Conference held in Rennes, France, June 24–28, 1991

Manfred Knebusch (auth.), Michel Coste, Louis Mahé, Marie-Françoise Roy (eds.)9783540559924, 3540559922

Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade – see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br|cker; G.W. Brumfield; A. Castilla; Z. Charzynski and P. Skibinski; M. Coste and M. Reguiat; A. Degtyarev; Z. Denkowska; J.-P. Francoise and F. Ronga; J.M. Gamboa and C. Ueno; D. Gondard- Cozette; I.V. Itenberg; P. Jaworski; A. Korchagin; T. Krasinksi and S. Spodzieja; K. Kurdyka; H. Lombardi; M. Marshall and L. Walter; V.F. Mazurovskii; G. Mikhalkin; T. Mostowski and E. Rannou; E.I. Shustin; N. Vorobjov.

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Table of contents :
Semialgebraic topology in the last ten years….Pages 1-36
Algebraic geometric methods in real algebraic geometry….Pages 37-51
On the classification of decomposing plane algebraic curves….Pages 52-74
Real algebra and its applications to geometry in the last ten years: Some major developments and results….Pages 75-96
Topology of real plane algebraic curves….Pages 97-109
Moduli problems in real algebraic geometry….Pages 110-119
Constructing strange real algebraic sets….Pages 120-127
More on basic semialgebraic sets….Pages 128-139
Mirror property for nonsingular mixed configurations of one line and k points in R 3 ….Pages 140-144
Families of semialgebraic sets and limits….Pages 145-162
A hopf fixed point theorem for semi-algebraic maps….Pages 163-169
On regular open semi-algebraic sets….Pages 170-173
Sums of 2n-th powers meromorphic functions with compact zero set….Pages 174-177
Pseudoorthogonality of powers of the coordinates of a holomorphic mapping in two variables with the constant Jacobian….Pages 178-192
Trivialités en famille….Pages 193-204
Stiefel orientations on a real algebraic variety….Pages 205-220
Subanaliticity and the second part of Hilbert’s 16 th problem….Pages 221-234
The decidability of real algebraic sets by the index formula….Pages 235-239
Proper polynomial maps: The real case….Pages 240-256
Sur les ordres de niveau 2 n et sur une extension du 17ème probleme de Hilbert….Pages 257-266
Curves of degree 6 with one non-degenerate double point and groups of monodromy of non-singular curves….Pages 267-288
The 17-th Hilbert problem for noncompact real analytic manifolds….Pages 289-295
Construction of new M-curves of 9-th degree….Pages 296-307
On linear differential operators related to the n-dimensional jacobian conjecture….Pages 308-315
On a subanalytic stratification satisfying a Whitney property with exponent 1….Pages 316-322
Une borne sur les degres pour le theoreme des zeros reel effectif….Pages 323-345
Minimal generation of basic semi-algebraic sets over an arbitrary ordered field….Pages 346-353
Configurations of at most 6 lines of ℙ P 3 ….Pages 354-371
Extensions of Rokhlin congruence for curves on surfaces….Pages 372-377
Complexité de la construction des strates à multiplicité constante d’un ensemble algébrique de ℂ n ….Pages 378-388
Real plane algebraic curves with many singularities….Pages 389-401
Effective stratification of regular real algebraic varieties….Pages 402-415