On the Equations Defining Abelian Varieties. III.
On the Euler Characteristic of Complex Algebraic Varieties.
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 characteristic of the links of a set determined by smooth definable functions
The purpose of this paper is to carry over to the o-minimal settings some results about the Euler characteristic of algebraic and analytic sets. Consider a polynomially bounded o-minimal structure on the field ℝ of reals. A () smooth definable function φ: U → ℝ on an open set U in ℝⁿ determines two closed subsets W := u ∈ U: φ(u) ≤ 0, Z := u ∈ U: φ(u) = 0. We shall investigate the links of the sets W and Z at the points u ∈ U, which are well defined up to a definable homeomorphism. It is proven...
On the Euler characteristic of the real Milnor fibres of an analytic function
The paper is concerned with the relations between real and complex topological invariants of germs of real-analytic functions. We give a formula for the Euler characteristic of the real Milnor fibres of a real-analytic germ in terms of the Milnor numbers of appropriate functions.
On the Euler number of an orbifold.
On the Euler-Poincaré characteristics of finite dimensional -adic Galois representations
On the Exceptional Tangents to a Smooth, Plane Curve.
On the existence of abelian varieties with good reduction.
On the Existence of Analytic Contractions.
On the existence of certain families of curves.
On the Existence of Certain Smooth Toric Varieties.
On the existence of components of the Hilbert scheme with the expected number of moduli.
On the existence of components of the Noether-Lefschetz Locus with given codiemsnion.
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 curves with maximal rank in Pn.
On the existence of k-normal curves of given degree and genus in projective spaces.
We find some ranges for the 4-tuples of integers (d,g,n,r) for which there is a smooth connected non-degenerate curve of degree d and genus g, which is k-normal for every k ≤ r.
On the existence of special divisors on singular curves
on the existence of stable rank-2 sheaves on algebraic surfaces