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On the classification of OADP varieties

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Abstract

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following Pirio and Russo (Comm Math Helv, to appear), the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133, Roma, Italy

    Ciro Ciliberto

  2. Dipartimento di Matematica, Università di Catania, Viale A. Doria 6, 95125, Catania, Italy

    Francesco Russo

Authors
  1. Ciro Ciliberto
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  2. Francesco Russo
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Correspondence to Ciro Ciliberto.

Additional information

To Professor F. Catanese on the Occasion of his 60th Birthday

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Ciliberto, C., Russo, F. On the classification of OADP varieties. Sci. China Math. 54, 1561–1575 (2011). https://doi.org/10.1007/s11425-010-4164-7

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  • DOI: https://doi.org/10.1007/s11425-010-4164-7

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