On the generic injectivity of the Gauss map in positive characteristic.
On the geometry of conjugacy classes in classical groupes.
On the geometry of the sequence of infinitely near points.
On the homotopy of the complement to plane algebraic curves.
On the hypersurfaces containing a general projective curve
On the intersection multiplicity of images under an etale morphism
We present a formula for the intersection multiplicity of the images of two subvarieties under an etale morphism between smooth varieties over a field k. It is a generalization of Fulton's Example 8.2.5 from [3], where a strong additional assumption has been imposed. In a special case where the base field k is algebraically closed and a proper component of the intersection is a closed point, intersection multiplicity is an invariant of etale morphisms. This corresponds with analytic geometry where...
On the intersection multiplicity of improper components in algebraic geometry
On the intrinsic geometry of a unit vector field
We study the geometrical properties of a unit vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle with the Sasaki metric. For the case of constant curvature , we give a description of the totally geodesic unit vector fields for and and prove a non-existence result for . We also found a family of vector fields on the hyperbolic 2-plane of curvature which generate foliations on with leaves of constant intrinsic...
On the iteration of the adjunction process for surfaces of negative Kodaira dimension.
On the Jung method in positive characteristic
Let be a germ of normal surface with local ring covering a germ of regular surface with local ring of characteristic . Given an extension of valuation rings birationally dominating , we study the existence of a new such pair of local rings birationally dominating , such that is regular and has only toric singularities. This is achieved when is defectless or when is equal to
On the Kodaira Dimension of Minimal Threefolds.
On the Kodaira Dimension of the Moduli Space of Curves.
On the length of a extremal rational curve.
On the length of the absolute Samuel stratum
On the Łojasiewicz Exponent near the Fibre of a Polynomial
The equivalence of the definitions of the Łojasiewicz exponent introduced by Ha and by Chądzyński and Krasiński is proved. Moreover we show that if the above exponents are less than -1 then they are attained at a curve meromorphic at infinity.
On the Łojasiewicz exponent of the gradient of a polynomial function
Let be a polynomial with complex coefficients. The Łojasiewicz exponent of the gradient of h at infinity is the least upper bound of the set of all real λ such that in a neighbourhood of infinity in ℂ², for c > 0. We estimate this quantity in terms of the Newton diagram of h. Equality is obtained in the nondegenerate case.
On the Mapping Problem for Algebraic Real Hypersurfaces.
On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions
In this paper, we show that if and are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if is a holomorphic mapping defined near a neighborhood of so that , then is also algebraic. Our proof is based on a careful analysis on the invariant varieties and reduces to the consideration of many cases. After a slight modification, the argument is also used to prove a reflection principle, which allows our main result to be stated for mappings...
On the Minimal Models of Complex Manifolds.
On the minimality of hyperplane sections of projective threefolds.