Viro method for the construction of real complete intersections

Advances in Mathematics

Volumn 169, Issue 2, 2002, Pages 177-186

  Bihan, F ^a  

^a UNIVERSITY OF LAUSANNE   (Switzerland)

Author keywords

Topology of real algebraic varieties; Toric varieties; Viro method

Indexed keywords

EID: 0037055873     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.2001.2059     Document Type: Article

References (21)

1. F. Bihan, Betti numbers of real numerical quintic surfaces, in "Topology, Ergodic Theory, Real Algebraic Geometry. Rokhlin's Memorial," (V. Turaev and A. Vershik, Eds.), Amer. Math. Soc. Transl. Ser. 2, Vol. 202, pp. 31-38, 2001, AMS, Providence, RI.
2. F. Bihan, Une sextique de l'espace projectif réel avec un grand nombre d'anses, Rev. Math. Helv. 14 (2001), 439-461.
3. F. Bihan, Asymptotics of Betti numbers of real algebraic surfaces, Comment. Math. Helv., to appear.
4. F. Bihan, Doubles hypersurfaces réelles et asymptotiques de nombres de Betti, submitted for publication, 2001.
5. B. Chevallier, Secteurs et déformations locales des courbes réelles, Math. Ann. 307 (1997), 1-28.
6. I. Gelfand, M. Kapranov, and A. Zelevinsky, "Discriminants, Resultants and Multi-dimensional Determinants," Birkhauser, Boston, 1994.
7. B. Huber, J. Rambau, and F. Santos, The Cayley trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings, J. Eur. Math. Soc. 2 (2000), 179-198.
8. I. Itenberg, Counter-examples to Ragsdale Conjecture and T-curves, Cont. Math. (Proceedings, Michigan 1993) 1982 (1995), 55-72.
9. I. Itenberg, Topology of real algebraic T-surfaces, Rev. Mat. No. Suppl. 10 (1997), 131-152.
10. 3, Amer. Math. Soc. Transl. (2) 173 (1996), 111-118.
11. I. Itenberg and E. Shustin, Singular points and limit cycles of planar polynomial vector fields, Duke Math. J. 102 No. 1 (2000), 1-37.
12. I. Itenberg and O. Viro, Maximal real algebraic hypersurfaces of projective space, in preparation.
13. J.-J. Risler, Construction d'hypersurfaces réelles [d'après Viro], in "Séminaire Bourbaki," Vol. 1992/93, Astérique no. 216, Exp. no. 763, 3, 1993, pp. 69-86.
14. M.-H. Schwartz, Champs radiaux sur une stratification analytique, in "Travaux en cours," Vol. 39, Hermann, Paris, 1991.
15. E. Shustin, Real plane algebraic curves with prescribed singularities, Topology 32 No. 4 (1993), 845-856.
16. E. Shustin, Critical points of real polynomials, subdivisions of Newton polyhedra and topology of real algebraic hypersurfaces, Amer. Math. Soc. Trans. (2) 173 (1996), 203-223.
17. B. Sturmfels, Viro's theorem for complete intersections, Ann. Scuola Norm. Sup. Pisa (4) 21 No. 3 (1994), 377-386.
18. B. Sturmfels, On the Newton polytope of the Resultant, J. Algebraic Combin. 3 (1994), 207-236.
19. O. Viro, Gluing of algebraic hypersurfaces, smoothing of singularities and construction of curves, in "Proceedings of the Leningrad International Topological Conference" Leningrad, August 1983, pp. 149-197, Nauka, Leningrad, 1983 (in Russian).
20. O. Viro, Gluing of Plane Algebraic Curves and Construction of Curves of Degree 6 and 7, Lecture Notes in Mathematics, Vol. 1060, pp. 187-200, Springer-Verlag, Berlin, Heidelberg, 1984.
21. O. Viro, Real algebraic plane curves: Constructions with controlled topology, Leningrad Math. J. 1 (1990), 1059-1134.