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On the irreducibility of Hilbert scheme of surfaces of minimal degree

100%

Bogomolov F., Kulikov V.

Open Mathematics

2013

tom 11

nr 2

254-263

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

100%

Bogomolov F., Kulikov V.

Open Mathematics

2012

tom 10

nr 2

521-529

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, 45(2), 137–148].

Ograniczanie wyników

2 Open Mathematics

2 Bogomolov F.

2 Kulikov V.

1 2013

1 2012

Wyniki wyszukiwania

On the irreducibility of Hilbert scheme of surfaces of minimal degree

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