On the existence of components of the Hilbert scheme with the expected number of moduli.
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 finiteness of rational curves on quintic threefolds
On the Hilbert Scheme of Curves in Higher-dimensional Projective Space.
On the Hilbert Scheme of Curves of Maximal Genus in a Projective Space.
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 homogeneous ideal of collinear punctual subschemes of P2.
On the homology of the Hubert scheme of points in the plane.
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 motive of an algebraic surface.
On the -conjecture
On the non-triviality of the Griffith group.
On the Normal Bundles of Rational Space Curves.
On the spannedness of adjunction of vector bundles.
On the Structure of the Birational Abel Morphism.
On the tautological ring of Mg.
On the Varieties Parametrizing Rational Space Curves with Fixed Normal Bundle.
Orbifold-Hodge numbers of Hilbert schemes