Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

On the irreducibility of Hilbert scheme of surfaces of minimal degree

Fedor Bogomolov;  Viktor Kulikov — 2013

Open Mathematics

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 diffeomorphic type of the complement to a line arrangement in a projective plane

Fedor Bogomolov;  Viktor Kulikov — 2012

Open Mathematics

We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011,...

Page 1

Download Results (CSV)