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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0130-7,
author = {Fedor Bogomolov and Viktor Kulikov},
title = {On the irreducibility of Hilbert scheme of surfaces of minimal degree},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {254-263},
zbl = {1262.14004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0130-7}
}
Fedor Bogomolov; Viktor Kulikov. On the irreducibility of Hilbert scheme of surfaces of minimal degree. Open Mathematics, Tome 11 (2013) pp. 254-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0130-7/
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