Algebraic geometry
Categorical characterization of quadrics
[Caractérisation catégorique des quadriques]
Comptes Rendus. Mathématique, Tome 356 (2018) no. 4, pp. 415-419.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.02.008
Li, Duo 1

1 Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, PR China
@article{CRMATH_2018__356_4_415_0,
     author = {Li, Duo},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2018.02.008/}
}
TY  - JOUR
AU  - Li, Duo
TI  - Categorical characterization of quadrics
JO  - Comptes Rendus. Mathématique
PY  - 2018
SP  - 415
EP  - 419
VL  - 356
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2018.02.008/
DO  - 10.1016/j.crma.2018.02.008
LA  - en
ID  - CRMATH_2018__356_4_415_0
ER  - 
%0 Journal Article
%A Li, Duo
%T Categorical characterization of quadrics
%J Comptes Rendus. Mathématique
%D 2018
%P 415-419
%V 356
%N 4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2018.02.008/
%R 10.1016/j.crma.2018.02.008
%G en
%F CRMATH_2018__356_4_415_0
Li, Duo. Categorical characterization of quadrics. Comptes Rendus. Mathématique, Tome 356 (2018) no. 4, pp. 415-419. doi : 10.1016/j.crma.2018.02.008. http://www.numdam.org/articles/10.1016/j.crma.2018.02.008/

[1] Araujo, C.; Druel, S.; Kovács, S.J. Cohomological characterizations of projective spaces and hyperquadrics, Invent. Math., Volume 174 (2008) no. 2, pp. 233-253

[2] Beilinson, A. Coherent sheaves on Pn and problems in linear algebra, Funkc. Anal. Prilozh., Volume 12 (1978) no. 3, pp. 68-69

[3] Bondal, A.I.; Polishchuk, A.E. Homological properties of associative algebras: the method of helices, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 57 (1993) no. 2, pp. 3-50

[4] Galkin, S.; Katzarkov, L.; Mellit, A.; Shinder, E. Minifolds and phantoms (preprint) | arXiv

[5] Galkin, S.; Shinder, E. Exceptional collections of line bundles on the Beauville surface, Adv. Math., Volume 244 (2013), pp. 1033-1050

[6] Kapranov, M. On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math., Volume 92 (1988) no. 3, pp. 479-508

[7] Kimura, S. 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] Kobayashi, S.; Ochiai, T. Characterizaions of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ., Volume 13 (1973), pp. 31-47

[9] Kuznetsov, A. Height of exceptional collections and Hochschild cohomology of quasiphantom categories, J. Reine Angew. Math., Volume 708 (2015), pp. 213-243

[10] Mori, A. Projective manifolds with ample tangent bundles, Ann. of Math. (2), Volume 110 (1979) no. 3, pp. 593-606

[11] Vial, C. Projectors on the intermediate algebraic Jacobians, N.Y. J. Math., Volume 19 (2013), pp. 793-822

[12] Vial, C. Exceptional collections, and the Néron–Severi lattice for surfaces, Adv. Math., Volume 305 (2017), pp. 895-934

Cité par Sources :