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Regular version of the site

Article

On the irreducibility of Hilbert scheme of surfaces of minimal degree

Central European Journal of Mathematics. 2013. Vol. 11. No. 2. P. 254-263.
Bogomolov F. A., Kulikov V. S.
The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙ m+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.