On the Euler characteristic of fibres of real polynomial maps
Let Y be a real algebraic subset of and be a polynomial map. We show that there exist real polynomial functions on such that the Euler characteristic of fibres of is the sum of signs of .
On the Euler characteristic of the link of a weighted homogeneous mapping
The paper is concerned with an effective formula for the Euler characteristic of the link of a weighted homogeneous mapping with an isolated singularity. The formula is based on Szafraniec’s method for calculating the Euler characteristic of a real algebraic manifold (as the signature of an appropriate bilinear form). It is shown by examples that in the case of a weighted homogeneous mapping it is possible to make the computer calculations of the Euler characteristics much more effective.
On the Euler number of an orbifold.
On the Euler-Poincaré characteristics of finite dimensional -adic Galois representations
On the existence of curves in with stable normal bundle
We prove that for integers n,d,g such that n ≥ 4, g ≥ 2n and d ≥ 2g + 3n + 1, the general (smooth) curve C in with degree d and genus g has a stable normal bundle .
on the existence of stable rank-2 sheaves on algebraic surfaces
On the ...-factor attached to motives.
On the Fundamental Group of a Unirational 3-Fold.
On the Fundamental Group of self-affine plane Tiles
Let be an expanding matrix, a set with elements and define via the set equation . If the two-dimensional Lebesgue measure of is positive we call a self-affine plane tile. In the present paper we are concerned with topological properties of . We show that the fundamental group of is either trivial or uncountable and provide criteria for the triviality as well as the uncountability of . Furthermore, we give a short proof of the fact that the closure of each component of is a locally...
On the fundamental group of the complement of a divisor in a homogeneous space.
On the Fundamental Group of the Space of Cubic Surfaces.
On the fundamental groups of some open rational surfaces.
On the Gauss maps of space curves in characteristic p
On the generation of certain bundles over P3.
On the Genus of Varieties of Codimension 2 in Projective Space.
On the geometry of a special determinantal hypersurface associated to the Mumford-Horrocks vector bundle.
On the Gieseker-Petri Map for Rank 2 vector bundles.
On the Growth of Cohomology Classes on Smooth Affine Varieties.
On the hard Lefschetz theorem in intersection homology for complex varieties with isolated singularities.
On the homology and cohomology of complete intersections with isolated singularities