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A few remarks on the Mohan Kumar theorem

100%

Jelonek Z.

2010

tom Vol. 58, no 3

197-200

We give a simple geometric proof of Mohan Kumar's result about complete intersections.

Topological characterization of finite mappings

100%

Jelonek Z.

2001

tom Vol. 49, no 3

279-283

In the paper [4] Krasiński and Spodzieja proved that if f : X -> Y is a Zariski closed non-constant mapping of affine varieties over C (where dim X [is greater than or equal to] 2), then f is finite. In this paper we generalize this result to the case of arbitrary algebraically closed field.

Smooth affine curves without embeddings into the affine plane

100%

Jelonek Z.

1999

tom Vol. 47, no 4

363-367

In this paper we gives examples of smooth affine curves which cannot be embedded in [C^2].

Injections into affine hypersurfaces

100%

Jelonek Z.

2000

tom Vol. 48, no 1

63-67

Let X be a smooth affine variety of dimension n > 2. Assume that the group H[sub 1](X,Z) is a torsion group and that [chi](X) = 1. Let Y be a projectively smooth affine hypersurface Y [is a subset of] C[sup n+1] of degree d > 1, which is smooth at infinity. Then there is no injective polynomial mapping f : X --> Y. This contradicts a result of Peretz [5].

A complement of a hypersurface in affine variety

100%

Jelonek Z.

2001

tom Vol. 49, no 4

375-379

We construct general examples of affine normal varieties X which have a hypersurface H [is a subset of] X, such that the variety X [...] H is not affine. We also show, that if X is an affine normal surface and H is a curve in X, then X [...] H is affine, too.

Note about the set S[f] for a polynomial mapping f : [C^2 --> C^2]

100%

Jelonek Z.

2001

tom Vol. 49, no 1

67-72

The aim of this paper is to give a simple method of computing the set S[f] of points at which a generically-finite polynomial mapping f : [C^2 --> C^2] is not proper.

Solving polynomial equations

100%

Jelonek Z.

2012

tom Vol. 45, nr 4

797-805

Let k be a field and (…) be a polynomial isomorphism. We give a formula for (…). In particular we show how to solve the equation (…).

A complete variety with infinitiely many maximal quasi-projective open subsets

63%

Farnik M. , Jelonek Z.

2010

tom Vol. 43, nr 2

277-284

Let K be an algebraically closed field. For every n>2 we find an n-dimensional complete variety Xn over K, which has infinitely many maximal quasi-projecive open subsets.