Algebraic Geometry/Homological Algebra
Beilinson resolutions on weighted projective spaces
[Résolutions de Beilinson sur espaces projectifs à poids]

Présenté par : Jean-Pierre Demailly

Canonaco, Alberto1
1 Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy
Comptes Rendus. Mathématique, Tome 336 (2003) no. 1, pp. 35-40.

On étend aux espaces projectifs à poids le théorème de Beilinson [Funct. Anal. Appl. 12 (1978) 214–216], qui décrit la catégorie derivée bornée des faisceaux cohérents sur ℙ n . Pour obtenir ce résultat on considère, au lieu de la catégorie habituelle des faisceaux cohérents, une certaine catégorie de faisceaux cohérents gradués (qui lui est équivalente dans le cas de ℙ n ).

Beilinson's theorem [Funct. Anal. Appl. 12 (1978) 214–216], which describes the bounded derived category of coherent sheaves on ℙ n , is extended to weighted projective spaces. This result is obtained by considering, instead of the usual category of coherent sheaves, a suitable category of graded coherent sheaves (which is equivalent in the case of ℙ n ).

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DOI : 10.1016/S1631-073X(02)00004-3
Canonaco, Alberto 1

1 Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy 
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Canonaco, Alberto. Beilinson resolutions on weighted projective spaces. Comptes Rendus. Mathématique, Tome 336 (2003) no. 1, pp. 35-40. doi : 10.1016/S1631-073X(02)00004-3. http://www.numdam.org/articles/10.1016/S1631-073X(02)00004-3/

[1] Baer, D. Tilting sheaves in representation theory of algebras, Manuscripta Math., Volume 60 (1988), pp. 323-347

[2] Beilinson, A.A. Coherent sheaves on ℙ n and problems of linear algebra, Funct. Anal. Appl., Volume 12 (1978), pp. 214-216

[3] Beilinson, A.A. The derived category of coherent sheaves on ℙ n , Selecta Math. Soviet., Volume 3 (1983–84), pp. 233-237

[4] Canonaco, A. A Beilinson-type theorem for coherent sheaves on weighted projective spaces, J. Algebra, Volume 225 (2000), pp. 28-46

[5] A. Canonaco, Beilinson resolutions on weighted projective spaces, Preprint, 2001

[6] Dolgachev, I. Weighted projective varieties, Proc. Vancouver 1981, Lecture Notes in Math., 956, Springer, 1982, pp. 34-71

[7] Hartshorne, R. Residues and Duality, Lecture Notes in Math., 20, Springer, Heidelberg, 1966

[8] Verdier, J.L. Des catégories derivées des catégories abéliennes, Astérisque, Volume 239 (1996)

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