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2012 | 10 | 4 | 1361-1379
Tytuł artykułu

On Buchsbaum bundles on quadric hypersurfaces

Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
Let E be an indecomposable rank two vector bundle on the projective space ℙn, n ≥ 3, over an algebraically closed field of characteristic zero. It is well known that E is arithmetically Buchsbaum if and only if n = 3 and E is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically Buchsbaum vector bundles on the smooth quadric hypersurface Q n ⊂ ℙn+1, n ≥ 3. We give in fact a full classification and prove that n must be at most 5. As to k-Buchsbaum rank two vector bundles on Q 3, k ≥ 2, we prove two boundedness results.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
4
Strony
1361-1379
Opis fizyczny
Daty
wydano
2012-08-01
online
2012-05-31
Twórcy
Bibliografia
  • [1] Ballico E., Valabrega P., Valenzano M., Non-vanishing theorems for rank two vector bundles on threefolds, Rend. Istit. Mat. Univ. Trieste, 2011, 43, 11–30
  • [2] Chang M.-C., Characterization of arithmetically Buchsbaum subschemes of codimension 2 in ℙn, J. Differential Geom., 1990, 31(2), 323–341
  • [3] Ein L., Sols I., Stable vector bundles on quadric hypersurfaces, Nagoya Math. J., 1984, 96, 11–22
  • [4] Ellia Ph., Fiorentini M., Quelques remarques sur les courbes arithmétiquement Buchsbaum de l’espace projectif, Ann. Univ. Ferrara Sez. VII, 1987, 33, 89–111
  • [5] Ellia Ph., Sarti A., On codimension two k-Buchsbaum subvarieties of ℙn, In: Commutative Algebra and Algebraic Geometry, Ferrara, Lecture Notes in Pure and Appl. Math., 206, Marcel Dekker, New York, 1999, 81–92
  • [6] Hernández R., Sols I., On a family of rank 3 bundles on Gr(1, 3), J. Reine Angew. Math., 1985, 360, 124–135
  • [7] Huybrechts D., Lehn M., The Geometry of Moduli Spaces of Sheaves, Aspects Math., Friedrich Vieweg & Sohn, Braunschweig, 1997
  • [8] Madonna C., A splitting criterion for rank 2 vector bundles on hypersurfaces in ℙ4, Rend. Semin. Mat. Univ. Politec. Torino, 1998, 56(2), 43–54
  • [9] Kumar N.M., Rao A.P., Buchsbaum bundles on ℙn, J. Pure Appl. Algebra, 2000, 152(1–3), 195–199 http://dx.doi.org/10.1016/S0022-4049(99)00129-2
  • [10] Ottaviani G., Spinor bundles on quadrics, Trans. Amer. Math. Soc., 1988, 307(1), 301–316 http://dx.doi.org/10.1090/S0002-9947-1988-0936818-5
  • [11] Ottaviani G., On Cayley bundles on the five-dimensional quadric, Boll. Un. Mat. Ital. A, 1990, 4(1), 87–100
  • [12] Ottaviani G., Szurek M., On moduli of stable 2-bundles with small Chern classes on Q 3, Ann. Mat. Pura Appl., 1994, 167(1), 191–241 http://dx.doi.org/10.1007/BF01760334
  • [13] Sols I., On spinor bundles, J. Pure Appl. Algebra, 1985, 35(1), 85–94 http://dx.doi.org/10.1016/0022-4049(85)90031-3
  • [14] Valenzano M., Rank 2 reflexive sheaves on a smooth threefold, Rend. Semin. Mat. Univ. Politec. Torino, 2004, 62(3), 235–254
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0005-y
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