Skip to main content

Varietes Toriques et Polytopes

  • Conference paper
  • First Online:
Séminaire Bourbaki vol. 1980/81 Exposés 561–578

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 901))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. A. D. ALEKSANDROV—On the theory of mixed volumes, 4 articles dans Mat. Sbornik, tomes 44 (p. 947–972 et 1205–1238) et 45 (p. 27–46 et 227–251) en 1937. Traduit par J. Firey, Dept. of Math, Oregon State University, Corvallis, Oregon 97331.

    Google Scholar 

  2. L. J. BILLERA et C. W. LEE—Suffciency of Mc Mullen's condition for f-vectors of simplicial polytopes. Bulletin A.M.S. Vol. 2, no 1 (1980) 181–185.

    Article  MATH  MathSciNet  Google Scholar 

  3. G. CLEMENTS et B. LINDSTRÖM—A generalization of a combinatorial theorem of Macaulay. Journ. Combinatorial Theory, 7 (1969) 230–238.

    MATH  Google Scholar 

  4. V. I. DANILOV—The geometry of toric varieties. Russian Math Surveys 33, 2 (1978) 97–154. Traduit de Uspekhi Mat. Nauk 33, 2, (1978), 85–134.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. DEMAZURE—Sous groupes algébriques de rang maximum du groupe de Cremona. Annales E.N.S. 4 ème série, t. 3 Fasc. 4 (1970).

    Google Scholar 

  6. F. EHLERS—Eine Klasse komplexer Mannig faltig keiten..., Math. Annalen, 218 (1975) 127–156.

    Article  MATH  MathSciNet  Google Scholar 

  7. C. GREENE and D. J. KLEITMAN—Proof techniques in the theory of finite sets “M.A.A. Studies in Combinatories” G. C. Rota, editor. Math. Assoc. of America, Washington, D. C. (1978).

    Google Scholar 

  8. G. GRÜNBAUM—Convex Polytopes, Wiley ed.

    Google Scholar 

  9. M. HOCHSTER—Cohen-Macaulay rings, Combinatorics and simplicial complexes. 2nd Oklahoma Ring Theory Conference, 171–223, Dekker 1978.

    Google Scholar 

  10. M. HOCHSTER—Rings of invariants of tori, Cohen—Macaulay rings generated by monomials, Annals of Math. 96 (1972) 318–337.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. G. HOVANSKI—Uspeki Mat. Nauk, 34, 4(208), p. 160–161.

    Google Scholar 

  12. M. N. ISHIDA—Torus embeddings and dualizing complexes. Tohôku Math. Journal 2nd series Vol. 32 no 1 (1980) 111–146.

    MATH  MathSciNet  Google Scholar 

  13. G. KEMPF et al.—Toroidal embeddings (Chap. 1), Springer Lecture Note 339.

    Google Scholar 

  14. F. S. MACAULAY—Some properties of enumeration in the theory of modular systems. Proc. Lond. Math. Soc. 26 (1927) 531–555.

    MATH  Google Scholar 

  15. P. Mc MULLEN—The maximum number of faces of a convex polytope. Mathematika 17 (1970) 179–184.

    Article  MathSciNet  Google Scholar 

  16. T. S. MOTZKIN—Comonotone curves and Polyhedra. Bull. Ann. Math. Soc. 63 (1957) 35.

    MathSciNet  Google Scholar 

  17. T. ODA—Torus embeddings and applications, Tata Institute, Bombay 1978.

    MATH  Google Scholar 

  18. P. SHENZEL—On the number of faces of simplicial complexes and the purity of Frobenius. Preprint, Martin-Luther Universität, Halle Wittenberg (R.D.R.) 1980.

    Google Scholar 

  19. G. C. SHEPARD—Inequalities between mixed volumes. Mathematika 7 (1960) 125–138.

    MathSciNet  Google Scholar 

  20. R. STANLEY—The number of faces of a simplicial convex polytope. Preprint, M.I.T. (1979).

    Google Scholar 

  21. R. STANLEY—The Hilbert function of a graded algebra, Advanced in Math., 28, no 1, (1978) 57–83.

    Article  MATH  MathSciNet  Google Scholar 

  22. R. STANLEY—The upper bound conjecture and Cohen Macaulay rings, Studies in Applied Math. 54 (1975) 135–142.

    MATH  MathSciNet  Google Scholar 

  23. R. STANLEY—Weyl groups, the hard Lefschetz theorem, and the Sperner property. S.I.A.M. Journal (1980).

    Google Scholar 

  24. J.H.M. STEENBRINK—Mixed Hodge structure on vanishing cohomology, Real and complex singularities, Oslo 1976, Noordhoff 1977.

    Google Scholar 

  25. B. TEISSIER—Du Théorème de l'index de Hodge aux inégalités isopérimétriques. C.R.A.S. Paris, tome 288 (29 Janvier 1979) 287–289.

    MATH  MathSciNet  Google Scholar 

  26. B. TEISSIER—Bonnesen type inequalities in algebraic geometry. Preprint, Harvard University et Centre de Math. de l'Ecole Polytechnique (1979).

    Google Scholar 

  27. B. TEISSIER—Jacobian polyhedra and equisingularity. Proceedings Conf. on singularities, R.I.M.S. Kyoto, April 1978. Publ. R.I.M.S. 1978.

    Google Scholar 

  28. L. A. SANTALO—Integral geometry and geometric probability, Encyclopedia of of mathematics and its applications, Addison-Wesley 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1981 N. Bourbaki

About this paper

Cite this paper

Teissier, B. (1981). Varietes Toriques et Polytopes. In: Séminaire Bourbaki vol. 1980/81 Exposés 561–578. Lecture Notes in Mathematics, vol 901. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097190

Download citation

  • DOI: https://doi.org/10.1007/BFb0097190

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11176-4

  • Online ISBN: 978-3-540-38956-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics