@incollection{SB_1993-1994__36__145_0, author = {Brion, Michel}, title = {Points entiers dans les polytopes convexes}, booktitle = {S\'eminaire Bourbaki : volume 1993/94, expos\'es 775-789}, series = {Ast\'erisque}, note = {talk:780}, pages = {145--169}, publisher = {Soci\'et\'e math\'ematique de France}, number = {227}, year = {1995}, mrnumber = {1321646}, zbl = {0847.52015}, language = {fr}, url = {http://www.numdam.org/item/SB_1993-1994__36__145_0/} }
TY - CHAP AU - Brion, Michel TI - Points entiers dans les polytopes convexes BT - Séminaire Bourbaki : volume 1993/94, exposés 775-789 AU - Collectif T3 - Astérisque N1 - talk:780 PY - 1995 SP - 145 EP - 169 IS - 227 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1993-1994__36__145_0/ LA - fr ID - SB_1993-1994__36__145_0 ER -
%0 Book Section %A Brion, Michel %T Points entiers dans les polytopes convexes %B Séminaire Bourbaki : volume 1993/94, exposés 775-789 %A Collectif %S Astérisque %Z talk:780 %D 1995 %P 145-169 %N 227 %I Société mathématique de France %U http://www.numdam.org/item/SB_1993-1994__36__145_0/ %G fr %F SB_1993-1994__36__145_0
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. http://www.numdam.org/item/SB_1993-1994__36__145_0/
[Bi1] Some theorems on actions of algebraic groups, Ann. of Math. 98, 480-497 (1973). | DOI | MR | Zbl
:[Bi2] 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). | MR | Zbl
:[Bo-Se] Le théorème de Riemann-Roch (d'après Grothendieck), Bull. Soc. Math. France 86, 97-136, 1958. | DOI | EuDML | Numdam | MR | Zbl
, :[Ca] Décomposition des polyèdres: le point sur le troisième problème de Hilbert, Sém. Bourbaki, exp. n° 646 (juin 1985), Astérisque 133-134, 1986, 261-288. | EuDML | Numdam | MR | Zbl
:[CaSh] Genera of algebraic varieties and counting of lattice points, preprint 1993. | MR | Zbl
, :[Da] The geometry of toric varietes, Russian Math. Surveys 33, 97-154, 1978. | DOI | MR | Zbl
:[Eh1] Sur un problème de géométrie diophantienne linéaire I. Polyèdres et réseaux, J. Reine Angew. Math. 226, 1-29, 1967. | EuDML | MR | Zbl
:[Eh2] Nombre de points entiers d'un tétraèdre, C. R. Acad. Sci. Paris, t. 258, Série I, 3945-3948, 1964. | MR | Zbl
:[Eh3] Démonstration de la loi de réciprocité pour le polyèdre convexe entier, C. R. Acad. Sci. Paris, t. 265, Série I, 5-7, 1967. | MR | Zbl
:[Eh4] Polynômes arithmétiques et méthode des polyèdres en combinatoire, International series of numerical mathematics 35, Birkhäuser 1977. | MR | Zbl
:[Fu1] Intersection theory, Springer-Verlag 1984. | DOI | MR | Zbl
:[Fu2] Introduction to toric varieties, Annals of Mathematical Studies 131, Princeton University Press 1993. | MR | Zbl
:[Hi]
: Ehrhart polynomials of convex polytopes, h-vectors of simplicialcomplexes, and nonsingular projective toric varieties, dans: Discrete and computational geometry, 165-177, Amer. Math. Soc., Providence 1991. | MR
[Ka] Sur le polynôme associé à un polytope à sommets entiers dans Rn, C. R. Acad. Sci. Paris, t. 314, Série I, 669-672, 1992. | MR | Zbl
:[KK1] Integral points in convex polyhedra, combinatorial Riemann-Roch theorem and generalized Euler-MacLaurin formula, prépublication de l'I.H.E.S., juin 1992.
, :[KK2] 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. | MR | Zbl
, :[Kl] Vector bundles on Demazure models, Sel. Math. Sov. 3, 41-44, 1983/84. | MR | Zbl
:[La] Weighted complete intersections and lattice points, preprint 1993. | MR | Zbl
:[Mc1] The polytope algebra, Adv. in Math. 78, 76-130, 1989. | DOI | MR | Zbl
:[Mc2] Valuations and dissections, dans: Handbook of Convex Geometry, Volume B, 933-988, North-Holland 1993. | DOI | MR | Zbl
:[McSc] Valuations on convex bodies, dans: Convexity and its applications, édité par P. M. Gruber et J. M. Wills, Birkhuser 1983. | MR | Zbl
, :[Mord] Lattice points in a tetrahedron and generalized Dedekind sums, J. Indian Math. Soc. 15, 41-46, 1951. | MR | Zbl
:[M1] A theory of polyhedra, Adv. in Math. 97, 1-73, 1993. | DOI | MR | Zbl
:[M2] Translation scissors congruence, Adv. in Math. 100, 1-27, 1993. | DOI | MR | Zbl
:[M3] The K-theory of a toric variety, Adv. in Math. 100, 154-182, 1993. | DOI | MR | Zbl
:[M4] The Todd class of a toric variety, Adv. in Math. 100, 182-231, 1993. | MR | Zbl
:[Od] Convex bodies and algebraic geometry. An introduction to the theory of torus embeddings, Springer-Verlag 1988. | EuDML | MR | Zbl
:[Pi] Geometrisches zur Zahlenlehre, Naturwiss. Z. Logos, Prag. 311-319, 1899. | JFM
:[Po] Toric varieties, lattice points and Dedekind sums, Math. Ann. 295, 1-24, 1993. | DOI | EuDML | MR | Zbl
:[PK1] Finitely additive measures of virtual polytopes, St. Petersburg Math. J. 4, 337-356, 1993. | MR | Zbl
, :[PK2] A Riemann-Roch theorem for integrals and sums of quasipolynomials over virtual polytopes, St. Petersburg Math. J. 4, 789-812, 1993. | MR | Zbl
, :[Ra] Generalization of the reciprocity formula for the Dedekind sums, Duke Math. J. 21, 391-398, 1954. | DOI | MR | Zbl
:[RaGr] Dedekind sums, Carus Math. Monogr. 16, Washington, Mathematical Association of America 1972. | MR | Zbl
, :[Re] On the volume of lattice polyhedra, Proc. London Math. Soc. (3) 7, 378-395, 1957. | DOI | MR | Zbl
:[St] On the Hilbert function of a graded Cohen-Macaulay domain, J. Pure Appl. Alg. 73, 307-314, 1991. | DOI | MR | Zbl
:[Te] Variétés toriques et polytopes, Sém. Bourbaki, exp. n° 565 (novembre 1980), Lect. Notes in Math. 901, 1981, 71-84. | EuDML | Numdam | MR | Zbl
:[Th] 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. | MR | Zbl
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