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2012 | 10 | 4 | 1380-1392
Tytuł artykułu

ACM bundles, quintic threefolds and counting problems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We review some facts about rank two arithmetically Cohen-Macaulay bundles on quintic threefolds. In particular, we separate them into seventeen natural classes, only fourteen of which can appear on a general quintic. We discuss some enumerative problems arising from these.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
4
Strony
1380-1392
Opis fizyczny
Daty
wydano
2012-08-01
online
2012-05-31
Twórcy
autor
Bibliografia
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  • [4] Chiantini L., Faenzi D., Rank 2 arithmetically Cohen-Macaulay bundles on a general quintic surface, Math. Nachr., 2009, 282(12), 1691–1708 http://dx.doi.org/10.1002/mana.200610825
  • [5] Chiantini L., Madonna C., ACM bundles on a general quintic threefold, Matematiche (Catania), 2000, 55(2), 239–258
  • [6] Clemens H., Kley H.P., On an example of Voisin, Michigan Math. J., 2000, 48, 93–119 http://dx.doi.org/10.1307/mmj/1030132710
  • [7] Ellingsrud G., Strømme S.A., Bott’s formula and enumerative geometry, J. Amer. Math. Soc., 1996, 9(1), 175–193 http://dx.doi.org/10.1090/S0894-0347-96-00189-0
  • [8] Grayson D.R., Stillman M.E., Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/
  • [9] Johnsen T., Kleiman S.L., Rational curves of degree at most 9 on a general quintic threefold, Comm. Algebra, 1996, 24(8), 2721–2753
  • [10] Katz S., On the finiteness of rational curves on quintic threefolds, Compositio Math., 1986, 60(2), 151–162
  • [11] Kley H.P., Rigid curves in complete intersection Calabi-Yau threefolds, Compositio Math., 2000, 123(2), 185–208 http://dx.doi.org/10.1023/A:1002012414149
  • [12] Knutsen A.L., On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds, preprint available at http://arxiv.org/abs/1009.4419
  • [13] Kontsevich M., Enumeration of rational curves via torus actions, In: The Moduli Space of Curves, Texel Island, April 1994, Progr. Math., 129, Birkhäuser, Boston, 1995, 335–368 http://dx.doi.org/10.1007/978-1-4612-4264-2_12
  • [14] Madonna C., A splitting criterion for rank 2 vector bundles on hypersurfaces in ℙ4, Rend. Sem. Mat. Univ. Politec. Torino, 1998, 56(2), 43–54
  • [15] Mohan Kumar N., Rao A.P., Ravindra G.V., Arithmetically Cohen-Macaulay bundles on three dimensional hypersurfaces, Int. Math. Res. Not. IMRN, 2007, 8, #rnm025
  • [16] Mohan Kumar N., Rao A.P., Ravindra G.V., Arithmetically Cohen-Macaulay bundles on hypersurfaces, Comment. Math. Helv., 2007, 82(4), 829–843 http://dx.doi.org/10.4171/CMH/111
  • [17] Okonek Ch., Notes on varieties of codimension 3 in ℙN, Manuscripta Math., 1994, 84, 421–442 http://dx.doi.org/10.1007/BF02567467
  • [18] Thomas R.P., A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations, J. Differential Geom., 2000, 54(2), 367–438
  • [19] Vainsencher I., Avritzer D., Compactifying the space of elliptic quartic curves, In: Complex Projective Geometry, Trieste, June 19–24, 1989/Bergen, July 3–6, 1989, London Math. Soc. Lecture Note Ser., 179, Cambridge University Press, Cambridge, 1992, 47–58
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0017-7
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