ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 32, 55 Materov, Evgeni, Krasnoyarsk state university, Russia One estimate for dimesion of H^{n}(C^{n}\V, C) Let V be a smooth algebraic hypersurface in C^{n} given by zeros of polynomial f ∈ C[x_{1}, …, x_{n}]. Suppose that for V there exists a simplicial toric compactification X of C^{n} such that the intersection of closure \overline{V} in X is trasnsversal to the divisor D = X\T – a complement to the n-dimesional torus in X. There is an inequality: dim H^{n}(C^{n}\V, C) ≤ #(Δ_{∗} ∩ Z^{n}) for dimension of higher-dimensional cohomology group of complement C^{n}\V in terms of number of integral points in polytope Δ_{∗} constructed from Newton polytope of f.