Geodesic
Polyhedra of schemes and algebraic varieties
Sbornik. Mathematics, Tome 26 (1975) no. 1, pp. 137-149 
V. I. Danilov. Polyhedra of schemes and algebraic varieties. Sbornik. Mathematics, Tome 26 (1975) no. 1, pp. 137-149. http://geodesic.mathdoc.fr/item/SM_1975_26_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

With every good compactification of an algebraic variety we associate a polyhedron. We show that the homotopy type of this polyhedron does not depend on the compactification and hence is an invariant of the algebraic variety. Bibliography: 9 titles.

[1] E. Spener, Algebraicheskaya topologiya, izd-vo «Mir», Moskva, 1971 | MR

[2] P. Khilton, S. Uaili, Teoriya gomologii, izd-vo «Mir», Moskva, 1966

[3] G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat, Toroidal Embeddings, I, Lecture Notes in Math., no. 339, 1973 | MR

[4] Kh. Khironaka, “Razreshenie osobennostei algebraicheskikh mnogoobrazii nad polyami kharakteristiki nul”, Matematika, 9:6 (1965), 2–70

[5] S. Abhyankar, Resolution of singularities of embedded algebraic surfaces, New York, 1966 | MR

[6] M. A. Frumkin, “Filtratsiya v trekhmernoi gruppe Kremony”, Matem. sb., 90 (132) (1973), 196–213 | MR | Zbl

[7] A. Grothendieck, Cohomologie locale des faisceaux cohérentes et theoremes de lefschetz locaux et globaux, Amsterdam, 1968 | MR

[8] A. Grothendieck, J. Dieudonne, Elements de Géométrie algebrique, Publ. Math. IHES, no. 11, 1961

[9] N. Burbaki, Kommutativnaya algebra, izd-vo «Mir», Moskva, 1971 | MR