Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 254-263 |
| Number of pages | 10 |
| Journal | Central European Journal of Mathematics |
| Volume | 11 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 2013 |
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Keywords
- Hilbert scheme
- Irreducible projective algebraic surfaces of minimal degree
ASJC Scopus subject areas
- Mathematics(all)
Cite this
On the irreducibility of Hilbert scheme of surfaces of minimal degree. / Bogomolov, Fedor; Kulikov, Viktor S.
In: Central European Journal of Mathematics, Vol. 11, No. 2, 02.2013, p. 254-263.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the irreducibility of Hilbert scheme of surfaces of minimal degree
AU - Bogomolov, Fedor
AU - Kulikov, Viktor S.
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
UR - http://www.scopus.com/inward/record.url?scp=84870390535&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84870390535&partnerID=8YFLogxK
U2 - 10.2478/s11533-012-0130-7
DO - 10.2478/s11533-012-0130-7
M3 - Article
VL - 11
SP - 254
EP - 263
JO - Open Mathematics
JF - Open Mathematics
SN - 1895-1074
IS - 2
ER -