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2013 | 11 | 2 | 254-263
Tytuł artykułu

On the irreducibility of Hilbert scheme of surfaces of minimal degree

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EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
2
Strony
254-263
Opis fizyczny
Daty
wydano
2013-02-01
online
2012-11-21
Bibliografia
  • [1] Ciliberto C., Flamini F., On the branch curve of a general projection of a surface to a plane, Trans. Amer. Math. Soc., 2011, 363(7), 3457–3471 http://dx.doi.org/10.1090/S0002-9947-2011-05401-2
  • [2] Dolgachev I.V., Iskovskikh V.A., Finite subgroups of the plane Cremona group, In: Algebra, Arithmetic, and Geometry: in Honor of Yu. I. Manin, I, Progr. Math., 269, Birkhäuser, Boston, 2009, 443–548
  • [3] Griffiths P., Harris J., Principles of Algebraic Geometry, Pure Appl. Math. (N.Y.), John Wiley & Sons, New York, 1978
  • [4] Eisenbud D., Harris J., On varieties of minimal degree (a centennial account), In: Algebraic Geometry I, Brunswick, July 8–26, 1985, Proc. Sympos. Pure Math., 46(1), American Mathematical Society, Providence, 1987, 3–13
  • [5] Kulikov Vik.S., On Chisini’s conjecture, Izv. Math., 63(6), 1999, 1139–1170 (in Russian) http://dx.doi.org/10.1070/IM1999v063n06ABEH000267
  • [6] Kulikov Vik.S., On Chisini’s conjecture II, Izv. Math., 2008, 72(5), 901–913 (in Russian) http://dx.doi.org/10.1070/IM2008v072n05ABEH002423
  • [7] Kulikov Vik.S., A remark on classical Pluecker’s formulae, preprint available at http://arxiv.org/abs/1101.5042
  • [8] Kulikov V.S., Kulikov Vik.S., On complete degenerations of surfaces with ordinary singularities in ℙ3, Sb. Math., 2010, 201(1), 129–158 http://dx.doi.org/10.1070/SM2010v201n01ABEH004068
  • [9] Reid M., Chapters on algebraic surfaces, In: Complex Algebraic Geometry, Park City, 1993, IAS/Park City Math. Ser., 3, American Mathematical Society, Providence, 1997
  • [10] Semple J.G., Roth L., Introduction to Algebraic Geometry, Oxford, Clarendon Press, 1949
  • [11] Shafarevich I.R., Averbukh B.G., Vainberg Yu.R., Zhizhchenko A.B., Manin Yu.I., Moishezon B.G., Tyurina G.N., Tyurin A.N., Algebraic Surfaces, Trudy Mat. Inst. Steklov., 75, Nauka, Moscow, 1965 (in Russian)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0130-7
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