Beilinson resolutions on weighted projective spaces

Alberto Canonaco

doi:10.1016/S1631-073X(02)00004-3

Algebraic Geometry/Homological Algebra

Beilinson resolutions on weighted projective spaces
[Résolutions de Beilinson sur espaces projectifs à poids]

Présenté par : Jean-Pierre Demailly

Alberto Canonaco ¹

¹ Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy

Comptes Rendus. Mathématique, Volume 336 (2003) no. 1, pp. 35-40.

Résumé
Abstract

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 $ℙ^{n}$ ).

Reçu le : 2002-07-25
Accepté le : 2002-11-05
Publié le : 2003-01-01

DOI : 10.1016/S1631-073X(02)00004-3

Affiliations des auteurs :

Alberto Canonaco ¹

¹ Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy

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Alberto Canonaco. Beilinson resolutions on weighted projective spaces. Comptes Rendus. Mathématique, Volume 336 (2003) no. 1, pp. 35-40. doi : 10.1016/S1631-073X(02)00004-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)00004-3/

Bibliographie
Cité par

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Michael K. Brown; Daniel Erman A short proof of the Hanlon-Hicks-Lazarev theorem, Forum of Mathematics, Sigma, Volume 12 (2024), p. 6 (Id/No e56) | DOI:10.1017/fms.2024.40 | Zbl:1546.13025
Helmut Lenzing The algebraic theory of Fuchsian singularities, Advances in representation theory of algebras, ARTA VII. Conference in honor of José Antonio de la Peña's 60th birthday, Instituto de Matemáticas, Universidad Nacional Autónoma de Mexico City, Mexico, September 24–28, 2018, Providence, RI: American Mathematical Society (AMS); Montreal: Centre de Recherches Mathématiques (CRM), 2021, pp. 171-190 | DOI:10.1090/conm/761/15315 | Zbl:1481.14004
Alberto Canonaco Beilinson resolutions on weighted projective spaces., Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 336 (2003) no. 1, pp. 35-40 | DOI:10.1016/s1631-073x(02)00004-3 | Zbl:1042.18011

Cité par 3 documents. Sources : zbMATH

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