Key points are not available for this paper at this time.
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.
Danilov et al. (Thu,) studied this question.