On the Injectivity of the Map of the Witt Group of a Scheme into the Witt Group of its Function Field (Correction).
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 intersection of modular correspondences.
On the intersection of three quadrics.
On the intersection product of analytic cycles
We prove that the generalized index of intersection of an analytic set with a closed submanifold (Thm. 4.3) and the intersection product of analytic cycles (Thm. 5.4), which are defined in [T₂], are intrinsic. We define the intersection product of analytic cycles on a reduced analytic space (Def. 5.8) and prove a relation of its degree and the exponent of proper separation (Thm. 6.3).
On the irreducibility of Hilbert scheme of surfaces of minimal degree
The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙm+1 is irreducible except m = 4. In the case m = 4 the Hilbert scheme consists of two irreducible components explicitly described in the article. The main idea of our approach is to use the proof of Chisini conjecture [Kulikov Vik.S., On Chisini’s conjecture II, Izv. Math., 2008, 72(5), 901–913 (in Russian)] for coverings of projective plane branched in a special class of rational curves.
On the iteration of the adjunction process for surfaces of negative Kodaira dimension.
On the Kodaira Dimension of the Moduli Space of Curves.
On the Kodaira dimension of the moduli space of curves, II. The even-genus case.
On the k-regularity of some proyective manifolds.
The conjecture on the (degree-codimension + 1) - regularity of projective varieties is proved for smooth linearly normal polarized varieties (X,L) with L very ample, for low values of Delta(X,L) = degree-codimension-1. Results concerning the projective normality of some classes of special varieties including scrolls over curves of genus 2 and quadric fibrations over elliptic curves, are proved.
On the Lattice of Transcendental Cycles on an Elliptic Surface.
On the Lüroth Semigroup of curves lying on a smooth quadric.
On the minimality of hyperplane sections of projective threefolds.
On the mixed Hodge structure associated to of a simply connected complex projective manifold
On the Mixed Hodge Structure on the Cohomology of the Milnor Fibre.
On the motive of an algebraic surface.
On the -conjecture
On the Néron-Severi group of a singular variety.
On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold.