Viro theorem and topology of real and complex combinatorial hypersurfaces

Israel Journal of Mathematics

Volumn 133, Issue , 2003, Pages 189-238

  Itenberg, Ilia ^a   Shustin, Eugenii ^b  

^a CNRS   (France)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037256729     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02773068     Document Type: Article

References (42)

1. M. F. Atiyah, Convexity and commuting Hamiltonians. The Bulletin of the London Mathematical Society 14 (1982), 1-15.
2. M. F. Atiyah, Angular momentum, convex polyhedra and algebraic geometry, Proceedings of the Edinburgh Mathematical Society 26 (1983). 121-138.
3. M. F. Atiyah and I. M. Singer, The index of elliptic operators: III, Annals of Mathematics 87 (1968), 546-604.
4. G. E. Bredon, Introduction to Compact Transformation Groups (Pure and Applied Mathematics 46), Academic Press, New York, 1972.
5. R. Connelly and D. W. Henderson, A convex 3-complex not simplicially isomorphic to a strictly convex complex, Proceedings of the Cambridge Philosophical Society 88 (1980), 299-306.
6. V. I. Danilov and A. G. Khovanskii, Newton polyhedra and an algorithm for computing Hodge-Deligne numbers, Izvestiya Akademii Nauk SSSR 50 (1986), (Russian); English transl.: Mathematics of the USSR Izvestiya 29:2 (1987), 279298.
7. V. I. Danilov and A. G. Khovanskii, Newton polyhedra and an algorithm for computing Hodge-Deligne numbers, Izvestiya Akademii Nauk SSSR 50 (1986), (Russian); English transl.: Mathematics of the USSR Izvestiya 29:2 (1987), 279298.
8. A. Degtyarev and V. Kharlamov, Topological properties of real algebraic varieties: Rokhlin's way, Uspekhi Matematicheskikh Nauk 55 (2000), no. 4(334), 129-212 (Russian).
9. J. A. de Loera and F. J. Wicklin, On the need of convexity in patchworking, Advances in Applied Mathematics 20 (1998), 188-219.
10. I. Fary, Cohomologie des variétés algébriques, Annals of Mathematics 65 (1957), 21-73.
11. S. Fiedler-Le Touzé and S. Yu. Orevkov, A flexible affine M-sextic non-realizable algebraically, Journal of Algebraic Geometry 11 (2002), 293-310.
12. M. H. Freedman and F. Quinn, Topology of 4-manifolds (Princeton Mathematical Series 39). Princeton University Press, Princeton, NJ, 1990.
13. W. Fulton. Introduction to Toric Varieties (Annals of Mathematics Studies 131), Princeton University Press, Princeton, NJ, 1993.
14. I. M. Gelfand, M. M. Kapranov and A. V. Zelevinski, Discriminants, Resultants and Multidimensional Determinants, Birkhäuser, Boston, 1994.
15. M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Inventiones Mathematicae 82 (1985), 307-347.
16. D. A. Gudkov, Topology of real projective algebraic varieties, Russian Mathematical Surveys 29 (1974), 3-79.
17. B. Haas, The Ragsdale conjecture for maximal T-curves, Preprint, Universität Basel, 1997.
18. F. Hirzebruch, The signature of ramified coverings, in Global Analysis (Papers in honor of K. Kodaira), University of Tokyo Press, Tokyo, 1969, pp. 253-265.
19. F. Hirzebruch, The signature theorem: reminiscences and recreation, in Prospects in Mathematics (Annals of Mathematics Studies 70), Princeton University Press, Princeton, 1971, pp. 3-31.
20. I. Itenberg, Counterexamples to Ragsdale conjecture and T-curves, in Contemporary Mathematics 182 (Proc. Conf. Real Alg. Geom., December 17-21, 1993, Michigan, ed. S. Akbulut), AMS, Providence, RI, 1995, pp. 55-72.
21. I. Itenberg and E. Shustin, Combinatorial patchworking of real pseudo-holomorphic curves, Turkish Journal of Mathematics 26 (2002), 27-51.
22. I. Itenberg and O. Viro, Patchworking algebraic curves disproves the Ragsdale conjecture, The Mathematical Intelligencer 18 (1996), 19-28.
23. V. Kharlamov, New congruences for the Euler characteristic of real algebraic manifolds, Functional Analysis and its Applications 7 (1973), 147-150.
24. V. Kharlamov, Additional conruences for the Euler characteristic of even-dimensional real algebraic manifolds, Functional Analysis and its Applications 9 (1975), 134-141.
25. S. Yu. Orevkov, Link theory and oval arrangements of real algebraic curves, Topology 38 (1999), 779-810.
26. S. Yu. Orevkov and E. Shustin, Flexible, algebraically unrealizable curves: Rehabilitation of Hilbert-Rohn-Gudkov approach. Journal für die reine und angewandte Mathematik (2002), to appear.
27. P. Parenti, Combinatorics of dividing T-curves, Ph. D. Thesis, Università di Pisa, 1999.
28. J.-J. Risler, Construction d'Hypersurfaces réelles [d'Après Viro], Séminaire N. Bourbaki, no. 763. Vol. 1992-93, Novembre 1992.
29. V. A. Rokhlin, Congruences modulo 16 in Hilbert's 16th problem, Functional Analysis and its Applications 6 (1972), 301-306.
30. V. A. Rokhlin. Complex topological characteristics of real algebraic curves, Russian Mathematical Surveys 33 (1978), 85-98.
31. F. Santos, Improved counterexamples to the Ragsdale conjecture, Preprint, Universidad de Cantabria, 1994.
32. E. Shustin, Topology of real plane algebraic curves, in Proc. Intern. Conf. Real Algebraic Geometry, Rennes, June 24-29 1991, Lecture Notes in Mathematics 1524, Springer, Berlin, 1992, pp. 97-109.
33. O. Ya. Viro. Gluing of algebraic hypersurfaces, smoothing of singularities and construction of curves, in Proc. Leningrad Int. Topological Conf., Leningrad, Aug. 1982, Nauka, Leningrad, 1983, pp. 149-197 (Russian).
34. O. Ya. Viro. Gluing of plane real algebraic curves and construction of curves of degrees 6 and 7, Lecture Notes in Mathematics 1060, Springer, Berlin, 1984, pp. 187-200.
35. O. Ya. Viro, Real plane curves of degrees 7 and 8: new prohibitions, Mathematics of the USSR Izvestia 23 (1984), 409-422.
36. O. Ya. Viro, Progress in the topology of real algebraic varieties over the last six years, Russian Mathematical Surveys 41 (1986), 55-82.
37. O. Ya. Viro, Real algebraic plane curves: constructions with controlled topology, Leningrad Mathematical Journal 1 (1990), 1059-1134.
38. O. Ya. Viro, Mutual position of hypersurfaces in projective space, in Geometry of Differential Equations (American Mathematical Society Transl., Ser. 2, 186), American Mathematical Society, Providence, RI, 1998, pp. 161-176.
39. O. Ya. Viro, Patchworking real algebraic varieties. Available at http://www.math.uu.se/̃oleg/pw.ps.
40. 1. Proceedings of the London Mathematical Society (3) 85 (2002), 367-392.
41. G. Wilson, Hubert's sixteenth problem, Topology 17 (1978), 53-73.
42. G. Ziegler, Lectures on Polytopes (Graduate Texts in Mathematics 152), Springer-Verlag, Berlin, 1995.