Piecewise polynomial functions, convex polytopes and enumerative geometry
Brion, Michel
Banach Center Publications, Tome 37 (1996), p. 25-44 / Harvested from The Polish Digital Mathematics Library
Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:208580
@article{bwmeta1.element.bwnjournal-article-bcpv36z1p25bwm,
     author = {Brion, Michel},
     title = {Piecewise polynomial functions, convex polytopes and enumerative geometry},
     journal = {Banach Center Publications},
     volume = {37},
     year = {1996},
     pages = {25-44},
     zbl = {0878.14035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv36z1p25bwm}
}
Brion, Michel. Piecewise polynomial functions, convex polytopes and enumerative geometry. Banach Center Publications, Tome 37 (1996) pp. 25-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv36z1p25bwm/

[000] [1] M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28. | Zbl 0521.58025

[001] [2] D. N. Bernstein, The number of roots of a system of equations, Functional Anal. Appl. 9 (1975), 183-185.

[002] [3] E. Bifet, Cohomology, symmetry, and perfection, Publ. Mat. 36 (1992), 407-420. | Zbl 0809.14040

[003] [4] E. Bifet, C. DeConcini and C. Procesi, Cohomology of regular embeddings, Adv. Math. 82 (1990), 1-34. | Zbl 0743.14018

[004] [5] L. J. Billera, The algebra of piecewise polynomial functions, Adv. Math. 76 (1989), 170-183. | Zbl 0703.13015

[005] [6] L. J. Billera and L. L. Rose, Modules of piecewise polynomial functions and their freeness, Math. Z. 209 (1992), 485-497. | Zbl 0891.13004

[006] [7] M. Brion, Points entiers dans les polyèdres convexes, Ann. Scient. École Norm. Sup. (4) 21 (1988), 653-663.

[007] [8] M. Brion, Groupe de Picard et nombres caractéristiques des variétés sphériques, Duke Math. J. 58 (1989), 397-424. | Zbl 0701.14052

[008] [9] E. Casas-Alvero and S. Xambó-Descamps, The Enumerative Theory of Conics after Halphen, Lecture Notes in Math. 1196, Springer, Berlin, 1986. | Zbl 0626.14037

[009] [10] C. DeConcini and C. Procesi, Complete symmetric varieties II, in: Algebraic Groups and Related Topics, R. Hotta (ed.), Kinokuniya, Tokyo, 1985, 481-514.

[010] [11] A. Grothendieck and J. Dieudonné, Elements de géométrie algébrique I, Inst. Hautes Études Sci. Publ. Math. 4 (1960).

[011] [12] W. Fulton, Intersection theory, Springer, Berlin, 1984. | Zbl 0541.14005

[012] [13] W. Fulton, Introduction to toric varieties, Princeton University Press, 1993. | Zbl 0813.14039

[013] [14] W. Fulton and B. Sturmfels, Intersection theory on toric varieties, preprint 1994.

[014] [15] A. Hirschowitz, L'anneau de Chow équivariant, C. R. Acad. Sci. Paris Série I, 298 (1984), 87-89.

[015] [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.

[016] [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. | Zbl 0812.20023

[017] [18] A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math. 32 (1976), 1-31.

[018] [19] P. McMullen, The polytope algebra, Adv. Math. 78 (1989), 76-130. | Zbl 0686.52005

[019] [20] P. McMullen, Valuations and dissections, in: Handbook of convex geometry, Volume B, P. Gruber and J. Wills (eds.), North-Holland, 1993, 933-988. | Zbl 0791.52014

[020] [21] R. Morelli, A theory of polyhedra, Adv. Math. 97 (1993), 1-73. | Zbl 0779.52016

[021] [22] R. Morelli, The K-theory of a toric variety, Adv. Math. 100 (1993), 154-182. | Zbl 0805.14025

[022] [23] C. Procesi and S. Xambó-Descamps, On Halphen's first formula, in: Enumerative algebraic geometry (Copenhagen, 1989), Contemp. Math. 123 (1991), 199-211.

[023] [24] A. V. Pukhlikov and A. G. Khovanskii, Finitely additive measures of virtual polytopes, St. Petersburg Math. J. 4 (1993), 337-356. | Zbl 0791.52010

[024] [25] R. P. Stanley, Combinatorics and commutative algebra, Birkhäuser, Basel, 1983. | Zbl 0537.13009