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Newton polyhedra and an algorithm for computing Hodge–Deligne numbers

V. I. Danilov, A. G. Khovanskii


Abstract: 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.

UDC: 512.7

MSC: Primary 14F25, 14C30, 14L32; Secondary 32J25, 14J40, 52A25

Received: 13.07.1984

 English version: Mathematics of the USSR-Izvestiya, 1987, 29:2, 279–298

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