On the irreducibility of Hilbert scheme of surfaces of minimal degree

Fedor Bogomolov, Viktor S. Kulikov

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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.

Original languageEnglish (US)
Pages (from-to)254-263
Number of pages10
JournalCentral European Journal of Mathematics
Volume11
Issue number2
DOIs
StatePublished - Feb 1 2013

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Keywords

  • Hilbert scheme
  • Irreducible projective algebraic surfaces of minimal degree

ASJC Scopus subject areas

  • Mathematics(all)

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