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2 Bulletin of the Polish Academy of Sciences. Mathematics

2 Rams S.

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On intersections with hypersurfaces and normal pseudo-flatness

Rams S.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 3

335-340

We study the behaviour of the families of hypersurfaces that are applied in [4] to estimate the Łojasiewicz exponent and the exponent of separation at infinity. We prove that the hypersurfaces for which v((Z . H)^S, c) is minimal are to be smooth along a subset of Z [intersection of sets] S and to meet some algebraic cones along the tangent space to S.

Bezout-type theorems for certain analytic sets

Rams S.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 3

277-283

We give a formula for the total number of intersections of certain analytic subsets of cartesian products of holomorphically separable second-countable complex manifolds (Theorems 4.1, 4.2). We prove some stronger results for curves in cartesian products of open subsets of C (Theorem 4.3).