On the irreducibility of Hilbert scheme of surfaces of minimal degree

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• 作者：Fedor Bogomolov (1) (2)
  Viktor S. Kulikov (2) (3)
  
• 关键词：14C05 ; Hilbert scheme ; Irreducible projective algebraic surfaces of minimal degree
• 刊名：Central European Journal of Mathematics
• 出版年：2013
• 出版时间：February 2013
• 年：2013
• 卷：11
• 期：2
• 页码：254-263
• 全文大小：984KB
• 参考文献：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), 3457-471 <a class="external" href="http://dx.doi.org/10.1090/S0002-9947-2011-05401-2">CrossRefa>
  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, Birkh?user, Boston, 2009, 443-48
  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 8-6, 1985, Proc. Sympos. Pure Math., 46(1), American Mathematical Society, Providence, 1987, 3-3
  5. Kulikov Vik.S., On Chisini’s conjecture, Izv. Math., 63(6), 1999, 1139-170 (in Russian) <a class="external" href="http://dx.doi.org/10.1070/IM1999v063n06ABEH000267">CrossRefa>
  6. Kulikov Vik.S., On Chisini’s conjecture II, Izv. Math., 2008, 72(5), 901-13 (in Russian) <a class="external" href="http://dx.doi.org/10.1070/IM2008v072n05ABEH002423">CrossRefa>
  7. Kulikov Vik.S., A remark on classical Pluecker’s formulae, preprint available at <a class="a-plus-plus" href="http://arxiv.org/abs/1101.5042">http://arxiv.org/abs/1101.5042a>
  8. Kulikov V.S., Kulikov Vik.S., On complete degenerations of surfaces with ordinary singularities in ?sup class="a-plus-plus">3, Sb. Math., 2010, 201(1), 129-58 <a class="external" href="http://dx.doi.org/10.1070/SM2010v201n01ABEH004068">CrossRefa>
  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)
  
• 作者单位：Fedor Bogomolov (1) (2)
  Viktor S. Kulikov (2) (3)
  
  1. Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY, 10012, USA
  2. Laboratory of Algebraic Geometry, National Research University Higher School of Economics, Vavilova Str. 7, Moscow, Russia, 117312
  3. Steklov Mathematical Institute, Gubkina Str. 8, Moscow, Russia, 119991
  
• ISSN：1644-3616

文摘

The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ?sup class="a-plus-plus"> 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), 901-13 (in Russian)] for coverings of projective plane branched in a special class of rational curves.