Homological Projective Duality for Determinantal Varieties

Abstract : In this paper we prove Homological Projective Duality for crepant categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a n x m matrix of linear forms on a given projective space. As applications, we obtain pairs of derived-equivalent Calabi-Yau manifolds, and address a question by A. Bondal asking whether the derived category of any smooth projective variety can be fully faithfully embedded in the derived category of a smooth Fano variety. Moreover we discuss the relation between rationality and categorical representability in codimension two for determinantal varieties.
Type de document :
Pré-publication, Document de travail
23 pages, corrected a mistake, comments very welcome as usual. 2015
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https://hal.archives-ouvertes.fr/hal-01111000
Contributeur : Marie-Annick Guillemer <>
Soumis le : jeudi 29 janvier 2015 - 13:41:59
Dernière modification le : mercredi 12 juillet 2017 - 01:15:48

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  • HAL Id : hal-01111000, version 1
  • ARXIV : 1410.7803

Citation

Marcello Bernardara, Michele Bolognesi, Daniele Faenzi. Homological Projective Duality for Determinantal Varieties. 23 pages, corrected a mistake, comments very welcome as usual. 2015. <hal-01111000>

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