Geodesic
Exceptional Sets on Del~Pezzo Surfaces with One Log-Terminal Singularity
Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 36-51.

Voir la notice de l'article provenant de la source Math-Net.Ru

New full exceptional sets of coherent sheaves on a certain family of log-terminal del Pezzo surfaces, which is treated as a smooth stack, are constructed. These surfaces are not toroidal and can be represented as hypersurfaces in weighted projective 3-space.
Keywords: full exceptional set, category of coherent sheaves, bounded derived category, log-terminal singularity, projective space.
Mots-clés : del Pezzo surface 
@article{MZM_2007_82_1_a4,
     author = {A. Elagin},
     title = {Exceptional {Sets} on {Del~Pezzo} {Surfaces} with {One} {Log-Terminal} {Singularity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {36--51},
     publisher = {mathdoc},
     volume = {82},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a4/}
}
TY  - JOUR
AU  - A. Elagin
TI  - Exceptional Sets on Del~Pezzo Surfaces with One Log-Terminal Singularity
JO  - Matematičeskie zametki
PY  - 2007
SP  - 36
EP  - 51
VL  - 82
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a4/
LA  - ru
ID  - MZM_2007_82_1_a4
ER  - 
%0 Journal Article
%A A. Elagin
%T Exceptional Sets on Del~Pezzo Surfaces with One Log-Terminal Singularity
%J Matematičeskie zametki
%D 2007
%P 36-51
%V 82
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a4/
%G ru
%F MZM_2007_82_1_a4
A. Elagin. Exceptional Sets on Del~Pezzo Surfaces with One Log-Terminal Singularity. Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 36-51. http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a4/

[1] D. O. Orlov, “Proektivnye rassloeniya, monoidalnye preobrazovaniya i proizvodnye kategorii kogerentnykh puchkov”, Izv. RAN. Ser. matem., 56:4 (1992), 852–862 | MR | Zbl

[2] S. A. Kuleshov, D. O. Orlov, “Isklyuchitelnye puchki na poverkhnostyakh del Petstso”, Izv. RAN. Ser. matem., 58:3 (1994), 53–87 | MR | Zbl

[3] Y. Kawamata, Derived categories of toric varieties, arxiv: math.AG/0503102 | MR

[4] D. Auroux, L. Katzarkov, D. Orlov, Mirror symmetry for weighted projective planes and their noncommutative deformations, arxiv: math.AG/0404281

[5] A. I. Bondal, “Predstavleniya assotsiativnykh algebr i kogerentnye puchki”, Izv. AN SSSR. Ser. matem., 53:1 (1989), 25–44 | MR | Zbl

[6] W. Fulton, Introduction to toric varietes, Annals of Mathematics Studies, 131, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl

[7] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl

[8] H. Kojima, “Logarithmic Del Pezzo surfaces of rank one with unique singular points”, Japan. J. Math. (N.S.), 25:2 (1999), 343–375 | MR | Zbl

[9] M. Artin, J. J. Zhang, “Noncommutative Projective Schemes”, Adv. Math., 109:2 (1994), 228–287 | DOI | MR | Zbl

[10] D. Baer, “Tilting sheaves in representation theory of algebras”, Manuscripta Math., 60:3 (1988), 323–347 | DOI | MR | Zbl

[11] B. Keller, “Derived categories and their uses”, Handbook of Algebra, vol. 1, North-Holland, Amsterdam, 1996, 671–701 | MR | Zbl