Points entiers dans les polytopes convexes
Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 780, 25 p. 
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Brion, Michel. Points entiers dans les polytopes convexes, dans Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 780, 25 p.. https://www.numdam.org/item/SB_1993-1994__36__145_0/

[Bi1] A. Bialynicki-Birula: Some theorems on actions of algebraic groups, Ann. of Math. 98, 480-497 (1973). | Zbl | MR | DOI

[Bi2] A. Bialynicki-Birula: Some properties of the decomposition of algebraic varieties determined by actions of a torus, Bull. Acad. Polo. Ser. Sci. Math. Astronom. Phys. 24, 667-674 (1976). | Zbl | MR

[Bo-Se] A. Borel, J. P. Serre: Le théorème de Riemann-Roch (d'après Grothendieck), Bull. Soc. Math. France 86, 97-136, 1958. | Numdam | Zbl | MR | EuDML | DOI

[Ca] P. Cartier: Décomposition des polyèdres: le point sur le troisième problème de Hilbert, Sém. Bourbaki, exp. n° 646 (juin 1985), Astérisque 133-134, 1986, 261-288. | Numdam | Zbl | MR | EuDML

[CaSh] S. E. Cappell, J. L. Shaneson: Genera of algebraic varieties and counting of lattice points, preprint 1993. | MR | Zbl

[Da] V. I. Danilov: The geometry of toric varietes, Russian Math. Surveys 33, 97-154, 1978. | Zbl | MR | DOI

[Eh1] E. Ehrhart: Sur un problème de géométrie diophantienne linéaire I. Polyèdres et réseaux, J. Reine Angew. Math. 226, 1-29, 1967. | Zbl | MR | EuDML

[Eh2] E. Ehrhart: Nombre de points entiers d'un tétraèdre, C. R. Acad. Sci. Paris, t. 258, Série I, 3945-3948, 1964. | Zbl | MR

[Eh3] E. Ehrhart: Démonstration de la loi de réciprocité pour le polyèdre convexe entier, C. R. Acad. Sci. Paris, t. 265, Série I, 5-7, 1967. | Zbl | MR

[Eh4] E. Ehrhart: Polynômes arithmétiques et méthode des polyèdres en combinatoire, International series of numerical mathematics 35, Birkhäuser 1977. | Zbl | MR

[Fu1] W. Fulton: Intersection theory, Springer-Verlag 1984. | Zbl | MR | DOI

[Fu2] W. Fulton: Introduction to toric varieties, Annals of Mathematical Studies 131, Princeton University Press 1993. | Zbl | MR

[Hi] T. Hibi: Ehrhart polynomials of convex polytopes, h-vectors of simplicial

complexes, and nonsingular projective toric varieties, dans: Discrete and computational geometry, 165-177, Amer. Math. Soc., Providence 1991. | MR

[Ka] J. M. Kantor: Sur le polynôme associé à un polytope à sommets entiers dans Rn, C. R. Acad. Sci. Paris, t. 314, Série I, 669-672, 1992. | Zbl | MR

[KK1] J. M. Kantor, A. V. Khovanskii: Integral points in convex polyhedra, combinatorial Riemann-Roch theorem and generalized Euler-MacLaurin formula, prépublication de l'I.H.E.S., juin 1992.

[KK2] J. M. Kantor, A. V. Khovanskii: Une application du théorème de Riemann-Roch combinatoire au polynôme d'Ehrhart des polytopes entiers de Rd, C. R. Acad. Sci. Paris, t. 317, Série I, 501-507, 1993. | Zbl | MR

[Kl] A. A. Klyachko: Vector bundles on Demazure models, Sel. Math. Sov. 3, 41-44, 1983/84. | Zbl | MR

[La] R. Laterveer: Weighted complete intersections and lattice points, preprint 1993. | MR | Zbl

[Mc1] P. Mcmullen: The polytope algebra, Adv. in Math. 78, 76-130, 1989. | Zbl | MR | DOI

[Mc2] P. Mcmullen: Valuations and dissections, dans: Handbook of Convex Geometry, Volume B, 933-988, North-Holland 1993. | Zbl | MR | DOI

[McSc] P. Mcmullen, R. Schneider: Valuations on convex bodies, dans: Convexity and its applications, édité par P. M. Gruber et J. M. Wills, Birkhuser 1983. | Zbl | MR

[Mord] L. J. Mordell: Lattice points in a tetrahedron and generalized Dedekind sums, J. Indian Math. Soc. 15, 41-46, 1951. | Zbl | MR

[M1] R. Morelli: A theory of polyhedra, Adv. in Math. 97, 1-73, 1993. | Zbl | MR | DOI

[M2] R. Morelli: Translation scissors congruence, Adv. in Math. 100, 1-27, 1993. | Zbl | MR | DOI

[M3] R. Morelli: The K-theory of a toric variety, Adv. in Math. 100, 154-182, 1993. | Zbl | MR | DOI

[M4] R. Morelli: The Todd class of a toric variety, Adv. in Math. 100, 182-231, 1993. | Zbl | MR

[Od] T. Oda: Convex bodies and algebraic geometry. An introduction to the theory of torus embeddings, Springer-Verlag 1988. | Zbl | MR | EuDML

[Pi] G. Pick: Geometrisches zur Zahlenlehre, Naturwiss. Z. Logos, Prag. 311-319, 1899. | JFM

[Po] J. E. Pommersheim: Toric varieties, lattice points and Dedekind sums, Math. Ann. 295, 1-24, 1993. | Zbl | MR | EuDML | DOI

[PK1] A. V. Pukhlikov, A. G. Khovanskii: Finitely additive measures of virtual polytopes, St. Petersburg Math. J. 4, 337-356, 1993. | Zbl | MR

[PK2] A. V. Pukhlikov, A. G. Khovanskii: A Riemann-Roch theorem for integrals and sums of quasipolynomials over virtual polytopes, St. Petersburg Math. J. 4, 789-812, 1993. | Zbl | MR

[Ra] H. Rademacher: Generalization of the reciprocity formula for the Dedekind sums, Duke Math. J. 21, 391-398, 1954. | Zbl | MR | DOI

[RaGr] H. Rademacher, E. Grosswald: Dedekind sums, Carus Math. Monogr. 16, Washington, Mathematical Association of America 1972. | Zbl | MR

[Re] J. E. Reeve: On the volume of lattice polyhedra, Proc. London Math. Soc. (3) 7, 378-395, 1957. | Zbl | MR | DOI

[St] R. P. Stanley: On the Hilbert function of a graded Cohen-Macaulay domain, J. Pure Appl. Alg. 73, 307-314, 1991. | Zbl | MR | DOI

[Te] B. Teissier: Variétés toriques et polytopes, Sém. Bourbaki, exp. n° 565 (novembre 1980), Lect. Notes in Math. 901, 1981, 71-84. | Numdam | Zbl | MR | EuDML

[Th] R. W. Thomason: Algebraic K-theory of group scheme actions, dans: AIgebraic topology and algebraic K-theory, 539-563, Annals of Math. Studies 113, 1987, Princeton Univ. Press. | Zbl | MR