Algebraic geometry
Categorical characterization of quadrics

Presented by: Claire Voisin

Li, Duo1
1 Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, PR China
Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 415-419.

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.

Received:
Accepted:
Published online:
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 = {https://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  - https://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 https://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, Volume 356 (2018) no. 4, pp. 415-419. doi : 10.1016/j.crma.2018.02.008. https://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

Cited by Sources: