Let 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.
Soit 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.
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Alexander Samokhin 1
@article{CRMATH_2005__340_12_889_0, author = {Alexander Samokhin}, title = {On the derived category of coherent sheaves on a 5-dimensional {Fano} variety}, journal = {Comptes Rendus. Math\'ematique}, pages = {889--893}, publisher = {Elsevier}, volume = {340}, number = {12}, year = {2005}, doi = {10.1016/j.crma.2005.04.033}, language = {en}, }
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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⁎ This work was supported in part by the French Government fellowship and by the RFFI award No 02-01-22005.
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