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1
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Cyclic coverings of Fano threefolds

100%
Cynk S.
Annales Polonici Mathematici
|
2003
|
tom 80
|
nr 1
117-124
EN
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 $ϱ = h^{1,1}$.
2
Content available remote

Hodge numbers of a double octic with non-isolated singularities

100%
Cynk S.
Annales Polonici Mathematici
|
2000
|
tom 73
|
nr 3
221-226
EN
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.
3
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Injective endomorphisms of algebraic and analytic sets

64%
Cynk S., Rusek K.
Annales Polonici Mathematici
|
1991-1992
|
tom 56
|
nr 1
29-35
EN
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.
4
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Diagonal series of rational functions (several variables)

64%
Cynk S., Tworzewski P.
Annales Polonici Mathematici
|
1994
|
tom 59
|
nr 1
77-83
EN
We give representations of Nash functions in a neighbourhood of a polydisc (torus) in $ℂ^m$ as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in $ℂ^{m+1}$.
5
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Holomorphic bijections of algebraic sets

64%
Cynk S., Rusek K.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
63-66
EN
We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].
6
Content available remote

Diagonal series of rational functions

64%
Cynk S., Tworzewski P.
Annales Polonici Mathematici
|
1991
|
tom 55
|
nr 1
57-63
EN
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.
7
Content available remote

Double covers and Calabi-Yau varieties

64%
Cynk S., Szemberg T.
Banach Center Publications
|
1998
|
tom 44
|
nr 1
93-101
8
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A note on Liouville analytic spaces

38%
Cynk S.
Annales Polonici Mathematici
|
1990-1991
|
tom 52
|
nr 2
205-209
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