Proceedings of the American Mathematical Society

Author(s): Rosa Maria Miró-Roig; Helena Soares
Journal: Proc. Amer. Math. Soc. 136 (2008), 3751-3757.
MSC (2000): Primary 14F05
Posted: June 20, 2008
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Abstract: A very long-standing problem in Algebraic Geometry is to determine the stability of exceptional vector bundles on smooth projective varieties. In this paper we address this problem and we prove that any exceptional vector bundle on a smooth complete intersection

-fold $Y\subset\mathbb{P}^n$ of type $(d_1,\ldots,d_{n-3})$ with $d_1+\cdots+ d_{n-3}\leq n$ and $n\geq 4$ is stable.

1.: Brambilla, C., Cokernel bundles and Fibonacci bundles, Math. Nachr. (to appear).
2.: Costa, L., Miró-Roig, R. M., Tilting sheaves on toric varieties, Math. Z. 248 (2004), 849-865. MR 2103545 (2005m:14023)
3.: Costa, L., Miró-Roig, R. M., Derived categories of projective bundles, Proc. Amer. Math. Soc. 133, 9 (2005), 2533-2537. MR 2146195 (2006d:14017)
4.: Costa, L., Miró-Roig, R. M., Geometric collections and Castelnuovo-Mumford regularity, Math. Proc. Cambridge Philos. Soc. 143 (2007), 557-578.
5.: Drézet, J.-M., Fibrés exceptionnels et suite spectrale de Beilinson généralisée sur $\mathbb{P}_2(\mathbb{C})$ , Math. Ann. 275 (1986), 25-48. MR 849052 (88b:14014)
6.: Drézet, J.-M., Le Potier, J., Fibrés stables et fibrés exceptionnels sur $\mathbb{P}_{2}$ , Ann. Sci. École Norm. Sup. 18 (1985), 2, 193-243. MR 816365 (87e:14014)
7.: Gorodentsev, A. L., Exceptional bundles on surfaces with a moving anticanonical class, Math. USSR Isv. 33 (1989), 67-83. MR 966982 (90d:14017)
8.: Gorodentsev, A. L., Rudakov, A. N., Exceptional vector bundles on projective spaces, Duke Math. J. 54 (1987), 115-130. MR 885779 (88e:14018)
9.: Hartshorne, R., Stable reflexive sheaves, Math. Ann. 254 (1980), 121-176. MR 597077 (82b:14011)
10.: Kapranov, M. M., On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math. 92 (1988), 479-508. MR 939472 (89g:18018)
11.: Moıšezon, B. G., Algebraic homology classes on algebraic varieties, Math. USSR Izv. 1 (1967), 209-251. MR 0213351 (35:4215)
12.: Rudakov, A. N., Markov numbers and exceptional bundles on $\mathbb{P}^2$ , Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), 100-112; English transl. in Math. USSR Izv. 32 (1989). MR 936525 (89f:14012)
13.: Soares, H., Steiner bundles on the hyperquadric $Q_{n}\subset\mathbb{P}^{n+1}$ , $n\geq 3$ , Comm. Algebra 35 (2007), 4116-4136. MR 2372324
14.: Zube, D. Yu., The stability of exceptional bundles on three-dimensional projective space, in Helices and vector bundles, London Math. Soc. Lecture Notes Series, vol. 148 (1990), Cambridge Univ. Press, Cambridge. MR 1074787 (91j:14038)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14F05

Rosa Maria Miró-Roig
Affiliation: Facultat de Matemátiques, Departament d'Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
Email: miro@ub.edu

Helena Soares
Affiliation: ISCTE Business School, Departamento de Métodos Quantitativos, Edifício ISCTE, Av. Forças Armadas, 1649-026 Lisboa, Portugal
Email: helena.soares@ub.edu

DOI: 10.1090/S0002-9939-08-09258-7
PII: S 0002-9939(08)09258-7
Keywords: Exceptional vector bundles, stability
Received by editor(s): January 29, 2007,
Received by editor(s) in revised form: February 23, 2007
Posted: June 20, 2008
Additional Notes: The first author was partially supported by MTM2004-00666
The second author was partially supported by Fundação para a Ciência e Tecnologia under grant SFRH/BD/16589/2004, and by Departamento de Métodos Quantitativos do Instituto Superior de Ciências do Trabalho e da Empresa
Communicated by: Ted Chinburg
Copyright of article: Copyright 2008, American Mathematical Society

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