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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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Volume 11, Issue 2

Issues

Volume 13 (2015)

On the irreducibility of Hilbert scheme of surfaces of minimal degree

Fedor Bogomolov
  • Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY, 10012, USA
  • Laboratory of Algebraic Geometry, National Research University Higher School of Economics, Vavilova Str. 7, Moscow, Russia, 117312
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  • De Gruyter OnlineGoogle Scholar
/ Viktor Kulikov
  • Laboratory of Algebraic Geometry, National Research University Higher School of Economics, Vavilova Str. 7, Moscow, Russia, 117312
  • Steklov Mathematical Institute, Gubkina Str. 8, Moscow, Russia, 119991
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Published Online: 2012-11-21 | DOI: https://doi.org/10.2478/s11533-012-0130-7

Abstract

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.

MSC: 14C05

Keywords: Hilbert scheme; Irreducible projective algebraic surfaces of minimal degree

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About the article

Published Online: 2012-11-21

Published in Print: 2013-02-01


Citation Information: Open Mathematics, Volume 11, Issue 2, Pages 254–263, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-012-0130-7.

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© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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[1]
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[2]
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