If B is a surface in ℙ³ of degree 8 which is the union of two smooth surfaces intersecting transversally then the double covering of ℙ³ branched along B has a non-singular model which is a Calabi-Yau manifold. The aim of this note is to compute the Hodge numbers of this manifold.
We describe a series of Calabi-Yau manifolds which are cyclic coverings of a Fano 3-fold branched along a smooth divisor. For all the examples we compute the Euler characteristic and the Hodge numbers. All examples have small Picard number .
We give representations of Nash functions in a neighbourhood of a polydisc (torus) in as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in .
We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].
Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.
We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.
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