Download PDF - Piecewise polynomial functions, convex polytopes and enumerative geometryAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Piecewise polynomial functions, convex polytopes and enumerative geometry

Authors 1

Affiliations

  1. École Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 7, France

Bibliography

  1. M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28.
  2. D. N. Bernstein, The number of roots of a system of equations, Functional Anal. Appl. 9 (1975), 183-185.
  3. E. Bifet, Cohomology, symmetry, and perfection, Publ. Mat. 36 (1992), 407-420.
  4. E. Bifet, C. DeConcini and C. Procesi, Cohomology of regular embeddings, Adv. Math. 82 (1990), 1-34.
  5. L. J. Billera, The algebra of piecewise polynomial functions, Adv. Math. 76 (1989), 170-183.
  6. L. J. Billera and L. L. Rose, Modules of piecewise polynomial functions and their freeness, Math. Z. 209 (1992), 485-497.
  7. M. Brion, Points entiers dans les polyèdres convexes, Ann. Scient. École Norm. Sup. (4) 21 (1988), 653-663.
  8. M. Brion, Groupe de Picard et nombres caractéristiques des variétés sphériques, Duke Math. J. 58 (1989), 397-424.
  9. E. Casas-Alvero and S. Xambó-Descamps, The Enumerative Theory of Conics after Halphen, Lecture Notes in Math. 1196, Springer, Berlin, 1986.
  10. C. DeConcini and C. Procesi, Complete symmetric varieties II, in: Algebraic Groups and Related Topics, R. Hotta (ed.), Kinokuniya, Tokyo, 1985, 481-514.
  11. A. Grothendieck and J. Dieudonné, Elements de géométrie algébrique I, Inst. Hautes Études Sci. Publ. Math. 4 (1960).
  12. W. Fulton, Intersection theory, Springer, Berlin, 1984.
  13. W. Fulton, Introduction to toric varieties, Princeton University Press, 1993.
  14. W. Fulton and B. Sturmfels, Intersection theory on toric varieties, preprint 1994.
  15. A. Hirschowitz, L'anneau de Chow équivariant, C. R. Acad. Sci. Paris Série I, 298 (1984), 87-89.
  16. B. Y. Kazarnovskii, Newton polyhedra and the Bézout theorem for matrix-valued functions of finite-dimensional representations, Functional Anal. Appl. 21 (1987), 319-321.
  17. F. Knop, The Luna-Vust theory of spherical embeddings, in: Proceedings of the Hyderabad conference on algebraic groups, S. Ramanan (ed.), Manoj-Prakashan, Madras, 1991, 225-250.
  18. A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math. 32 (1976), 1-31.
  19. P. McMullen, The polytope algebra, Adv. Math. 78 (1989), 76-130.
  20. P. McMullen, Valuations and dissections, in: Handbook of convex geometry, Volume B, P. Gruber and J. Wills (eds.), North-Holland, 1993, 933-988.
  21. R. Morelli, A theory of polyhedra, Adv. Math. 97 (1993), 1-73.
  22. R. Morelli, The K-theory of a toric variety, Adv. Math. 100 (1993), 154-182.
  23. C. Procesi and S. Xambó-Descamps, On Halphen's first formula, in: Enumerative algebraic geometry (Copenhagen, 1989), Contemp. Math. 123 (1991), 199-211.
  24. A. V. Pukhlikov and A. G. Khovanskii, Finitely additive measures of virtual polytopes, St. Petersburg Math. J. 4 (1993), 337-356.
  25. R. P. Stanley, Combinatorics and commutative algebra, Birkhäuser, Basel, 1983.
Banach Center Publications
1996/36/1
Export to PBN, Opens in new tab
Pages:
25-44
Main language of publication
English
Published
1996
Exact and natural sciences