On the irreducibility of Hilbert scheme of surfaces of minimal degree

Fedor Bogomolov; Viktor S. Kulikov

doi:10.2478/s11533-012-0130-7

On the irreducibility of Hilbert scheme of surfaces of minimal degree

Fedor Bogomolov, Viktor S. Kulikov

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.2478/s11533-012-0130-7
State	Published - Feb 2013

Keywords

Hilbert scheme
Irreducible projective algebraic surfaces of minimal degree

ASJC Scopus subject areas

General Mathematics

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10.2478/s11533-012-0130-7

Cite this

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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.",

keywords = "Hilbert scheme, Irreducible projective algebraic surfaces of minimal degree",

author = "Fedor Bogomolov and Kulikov, {Viktor S.}",

note = "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.",

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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.

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On the irreducibility of Hilbert scheme of surfaces of minimal degree

Abstract

Keywords

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