Comptes Rendus
no. 12
Algebraic Geometry
On the derived category of coherent sheaves on a 5-dimensional Fano variety
[Sur la catégorie dérivée de faisceaux cohérents sur une variété de Fano de dimension 5]

Présenté par : Bernard Malgrange

Alexander Samokhin1
1 Département de mathématiques, LAGA (UMR 7539), institut Galilée, université Paris 13, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France
Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 889-893.

Soit LG3C la grassmannienne des plans lagrangiens dans un espace vectoriel V de dimension 6. C'est une variété de Fano d'indice 4. Considérons sa section lisse par un hyperplan. Nous montrons que dans la catégorie dérivée des faisceaux cohérents sur une telle section il existe une collection exceptionnelle qui engendre la catégorie dérivée.

Let LG3C be the Grassmannian of Lagrangian planes in a six-dimensional vector space V. It is a six-dimensional Fano variety of index 4. Consider its smooth hyperplane section. We show that in the derived category of coherent sheaves on such a hyperplane section there exists an exceptional collection, generating the derived category.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.04.033
Alexander Samokhin 1

1 Département de mathématiques, LAGA (UMR 7539), institut Galilée, université Paris 13, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France 
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Alexander Samokhin. On the derived category of coherent sheaves on a 5-dimensional Fano variety. Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 889-893. doi : 10.1016/j.crma.2005.04.033. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.04.033/

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[4] M. Kapranov On the derived category of coherent sheaves on some homogeneous spaces, Invent. Math., Volume 92 (1988), pp. 479-508

[5] M. Kontsevich Homological algebra of mirror symmetry, Proceedings of the International Congress of Mathematicians, vols. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, pp. 120-139

[6] A. Kuznetsov, Fano threefolds V22, preprint MPI, 24, 1997

[7] A. Kuznetsov, in preparation

[8] D. Orlov Exceptional set of vector bundles on the variety V5, Vestnik Moskov. Univ. Ser. I Mat. Mekh., Volume 5 (1991), pp. 69-71

[9] A. Samokhin The derived category of coherent sheaves on LG3C, Uspekhi Math. Nauk, Volume 56 (2001) no. 3, pp. 592-594

Cité par Sources :

⁎ This work was supported in part by the French Government fellowship and by the RFFI award No 02-01-22005.

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