TY - JOUR
T1 - On the irreducibility of Hilbert scheme of surfaces of minimal degree
AU - Bogomolov, Fedor
AU - Kulikov, Viktor S.
N1 - Funding Information:
The first author was supported by NSF grant DMS-1001662 and second author was partially supported by grants of NSh-4713.2010.1 and RFBR 11-01-00185. Both authors were supported by AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023.
PY - 2013/2
Y1 - 2013/2
N2 - 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.
AB - 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.
KW - Hilbert scheme
KW - Irreducible projective algebraic surfaces of minimal degree
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U2 - 10.2478/s11533-012-0130-7
DO - 10.2478/s11533-012-0130-7
M3 - Article
AN - SCOPUS:84870390535
SN - 1895-1074
VL - 11
SP - 254
EP - 263
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
IS - 2
ER -