On the Hilbert scheme of Palatini threefolds.
On the Hilbert scheme of points of an almost complex fourfold
If is a complex surface, one has for each the Hilbert scheme , which is a desingularization of the symmetric product . Here we construct more generally a differentiable variety endowed with a stable almost complex structure, for every almost complex fourfold . is a desingularization of the symmetric product .
On the Hodge conjecture for products of certain surfaces
On the Hodge cycles of Prym varieties
We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.
On the Hodge spectral sequence for some classes of non-complete algebraic manifolds.
On the hodge theory of the symmetric powers of a curve.
We describe the polarised Hodge structure on the symmetric powers of a smooth projective curve.
On the Hodge-Tage decomposition in the imperfect residue field case.
On the homogeneous ideal of collinear punctual subschemes of P2.
On the homogeneous ideal of unreduced projective schemes.
On the homology of the Hubert scheme of points in the plane.
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 Infinitesimal Torelli Theorem for Certain irregular Surfaces of General Type.
On the Injectivity of the Map of the Witt Group of a Scheme into the Witt Group of its Function Field.
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.