We give a characterization of smooth quadrics in terms of the existence of full exceptional collections of certain type, which generalizes a result of C.Vial for projective spaces.
En généralisant un résultat de C. Vial pour l'espace projectif, on donne une caractérisation des quadriques lisses en termes d'existence de collections pleines exceptionnelles d'un certain type.
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Duo Li 1
@article{CRMATH_2018__356_4_415_0, author = {Duo Li}, title = {Categorical characterization of quadrics}, journal = {Comptes Rendus. Math\'ematique}, pages = {415--419}, publisher = {Elsevier}, volume = {356}, number = {4}, year = {2018}, doi = {10.1016/j.crma.2018.02.008}, language = {en}, }
Duo Li. Categorical characterization of quadrics. Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 415-419. doi : 10.1016/j.crma.2018.02.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.02.008/
[1] Cohomological characterizations of projective spaces and hyperquadrics, Invent. Math., Volume 174 (2008) no. 2, pp. 233-253
[2] Coherent sheaves on and problems in linear algebra, Funkc. Anal. Prilozh., Volume 12 (1978) no. 3, pp. 68-69
[3] Homological properties of associative algebras: the method of helices, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 57 (1993) no. 2, pp. 3-50
[4] Minifolds and phantoms (preprint) | arXiv
[5] Exceptional collections of line bundles on the Beauville surface, Adv. Math., Volume 244 (2013), pp. 1033-1050
[6] On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math., Volume 92 (1988) no. 3, pp. 479-508
[7] Surjectivity of the cycle map for Chow motives, Motives and Algebraic Cycles, Fields Inst. Commun., vol. 56, American Mathematical Society, Providence, RI, USA, 2009, pp. 157-165
[8] Characterizaions of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ., Volume 13 (1973), pp. 31-47
[9] Height of exceptional collections and Hochschild cohomology of quasiphantom categories, J. Reine Angew. Math., Volume 708 (2015), pp. 213-243
[10] Projective manifolds with ample tangent bundles, Ann. of Math. (2), Volume 110 (1979) no. 3, pp. 593-606
[11] Projectors on the intermediate algebraic Jacobians, N.Y. J. Math., Volume 19 (2013), pp. 793-822
[12] Exceptional collections, and the Néron–Severi lattice for surfaces, Adv. Math., Volume 305 (2017), pp. 895-934
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