On the irreducibility of Hilbert scheme of surfaces of minimal degree

• Autorzy: Fedor Bogomolov , Viktor Kulikov
• Języki publikacji: 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.

Słowa kluczowe

EN

Hilbert scheme; Irreducible projective algebraic surfaces of minimal degree

Kategorie tematyczne

• 14C05: Parametrization (Chow and Hilbert schemes)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 2
• Strony: 254-263

Daty

wydano

2013-02-01

online

2012-11-21

Twórcy

autor

Fedor Bogomolov

autor

Viktor Kulikov

Bibliografia

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• [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
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• [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)

Identyfikatory

DOI

10.2478/s11533-012-0130-7