On completeness of varieties in enumerative geometry
On complex projective surfaces with trigonal hyperplane sections.
On contributions of embedded components to intersection theory. II.
On contributions of embedded components to intersection theory, a first approach
On degrees in multihomogeneous ideal theory.
On generalized Chern classes and Chern numbers of irreducible complex algebraic varieties with arbitrary singularities
On improper isolated intersection in complex analytic geometry
On intersection multiplicities in case of defect one
On Noether and strict stability, Hilbert exponent, and relative Nullstellensatz
Conditions characterizing the membership of the ideal of a subvariety arising from (effective) divisors in a product complex space Y × X are given. For the algebra of relative regular functions on an algebraic variety V, the strict stability is proved, in the case where Y is a normal space, and the Noether stability is established under a weakened condition. As a consequence (for both general and complete intersections) a global Nullstellensatz is derived for divisors in , respectively, . Also...
On polarized surfaces with small generalized class.
On the 2 and the 3-connectedness of ample divisors on a surface.
On the Affine Bezout Inequaltiy.
On the arithmetic Chern character
We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern class of the sequence and its Chern character with support on the finite fibers.Next, we compute these classes in the situation encountered by the second author when proving a “Kodaira vanishing theorem” for arithmetic...
On the characterization of Alexander schemes
On the Cohen-Macauly type of the general hypersurface section of a curve.
On the Exceptional Tangents to a Smooth, Plane Curve.
On the hard Lefschetz theorem in intersection homology for complex varieties with isolated singularities.
On the index of contact
We use the construction of the intersection product of two algebraic cones to prove that the multiplicity of contact of the cones at the vertex is equal to the product of their degrees. We give an example to show that in order to calculate the index of contact it is not sufficient to perform the analytic intersection algorithm with hyperplanes.
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