law Janeczko and Zbigniew Jelonek

Zbigniew Jelonek SOLVING POLYNOMIAL EQUATIONS

Injections into Affine Hypersurfaces )

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

A triterpene saponin from Lysimachia thyrsiflora L.

A triterpene saponoside (LTS-4) isolated from the underground parts of Lysimachia thyrsiflora L. was defined as 3-O-{beta-D-xylopyranosyl-(1 --> 2)-beta-D-glucopyranosyl-(1 --> 4)-[beta-D-glucopyranosyl-(1 --> 2)]-alpha-L-arabinopyranosyl}-cyclamiretin A. Structure assignment was performed on the basis of spectroscopic data including homo- and heteronuclear 1D and 2D NMR (COSY, TOCSY, NOESY, HE...

Linear Automorphisms That Are Symplectomorphisms

Let K be the field of real or complex numbers. Let (X ∼=K2n , ω) be a symplectic vector space and take 0<k<n,N =( 2n 2k ). Let L1, . . . , LN ⊂X be 2k-dimensional linear subspaces which are in a sufficiently general position. It is shown that if F :X −→X is a linear automorphism which preserves the form ωk on all subspaces L1, . . . , LN , then F is an k -symplectomorphism (that is, F ∗ω= kω, w...

Linearly Independent Divisors on Complex Manifolds )

Let X be a connected complex manifold and let D be a non-zero divisor on X with the support j D j : We show that if D is a principal divisor then the group H 1 (Xn j D j; Z) can not be a torsion group. In particular the group H 1 (Xn j D j; Z) must be innnite. As a corollary we prove that simple divisors D 1 ; :::; D r on a complex manifold X are linearly independent in C l(X), provided the gro...