Geodesic
Newton polyhedra and an algorithm for computing Hodge–Deligne numbers
Izvestiya. Mathematics, Tome 29 (1987) no. 2, pp. 279-298 
V. I. Danilov; A. G. Khovanskii. Newton polyhedra and an algorithm for computing Hodge–Deligne numbers. Izvestiya. Mathematics, Tome 29 (1987) no. 2, pp. 279-298. http://geodesic.mathdoc.fr/item/IM2_1987_29_2_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An algorithm is given for computing the mixed Hodge structure (more precisely, the Hodge–Deligne numbers) for cohomology of complete intersections in toric varieties in terms of Newton polyhedra specifying the complete intersection. In some particular cases the algorithm leads to explicit formulas. Bibliography: 8 titles.

[1] Delin P., “Teoriya Khodzha. II”, Matematika, 17:5 (1973), 3–57 | MR

[2] Deligne P., “Theorie de Hodge. III”, Publ. Math. IHES, 1974, no. 44, 5–77 | MR | Zbl

[3] Danilov V. I., “Geometriya toricheskikh mnogoobrazii”, Uspekhi matem. nauk, 33:2 (1978), 85–134 | MR | Zbl

[4] Khirtsebrukh F., Topologicheskie metody v algebraicheskoi geometrii, Mir, M., 1973

[5] Danilov V. I., “Mnogogranniki Nyutona i ischezayuschie kogomologii”, Funkts. analiz i ego prilozh., 13:2 (1979), 32–47 | MR | Zbl

[6] Khovanskii A. G., “Mnogogranniki Nyutona i toricheskie mnogoobraziya”, Funkts. analiz i ego prilozh., 11:4 (1977), 56–67 | MR

[7] Khovanskii A. G., “Mnogogranniki Nyutona i rod polnykh peresechenii”, Funkts. analiz i ego prilozh., 12:1 (1978), 51–61 | MR

[8] Kempf G., Knudsen F., Mumford D., Saint-Donat B., Toroidal Embeddings. I, Lecture Notes in Mathematics, 339, Springer-Verlag, Berlin, 1973 | MR | Zbl