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Tilting sheaves on toric varieties

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Abstract.

In [19], A. King states the following conjecture: Any smooth complete toric variety has a tilting bundle whose summands are line bundles. The goal of this paper is to prove King’s conjecture for the following types of smooth complete toric varieties: (i) Any d-dimensional smooth complete toric variety with splitting fan. (ii) Any d-dimensional smooth complete toric variety with Picard number ≤2. (iii) The blow up of any smooth complete minimal toric surface at T-invariants points.

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Acknowledgments.

The authors would like to thank Lutz Hille, Alastair King and Aidan Schofield for helpful discussions and to the referee for giving valuable advise on the presentation of the results.

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Authors and Affiliations

  1. Facultat de Matemàtiques, Departament d’Algebra i Geometria, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain

    L. Costa & R. M. Miró-Roig

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  1. L. Costa
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  2. R. M. Miró-Roig
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Correspondence to R. M. Miró-Roig.

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Mathematics Subject Classification (1991): 14F05; 14M25

Partially supported by BFM2001-3584.

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Costa, L., Miró-Roig, R. Tilting sheaves on toric varieties. Math. Z. 248, 849–865 (2004). https://doi.org/10.1007/s00209-004-0684-6

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  • DOI: https://doi.org/10.1007/s00209-004-0684-6

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