[Remarques sur les fibrés ACM de rang supérieur sur les hypersurfaces]
En termes de nombre de générateurs, le fibré de rang 3 arithmétiquement Cohen–Macaulay, non décomposé, le plus simple sur une hypersurface de , est engendré en rang 6. Nous montrons qu'une hypersurface générale dans , de degré , n'admet pas un tel fibré. Nous montrons également qu'une hypersurface lisse de dimension positive dans un espace projectif, de degré pair, n'admet pas de faisceau d'Ulrich de rang impair. Ceci permet de vérifier quelques cas de conjectures, que nous discutons ici.
In terms of the number of generators, one of the simplest non-split rank-3 arithmetically Cohen–Macaulay bundles on a smooth hypersurface in is 6-generated. We prove that a general hypersurface in of degree does not support such a bundle. We also prove that a smooth positive dimensional hypersurface in projective space of even degree does not support an Ulrich bundle of odd rank and determinant of the form for some integer c. This verifies some cases of conjectures we discuss here.
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@article{CRMATH_2018__356_11-12_1215_0,
author = {Girivaru V. Ravindra and Amit Tripathi},
title = {Remarks on higher-rank {ACM} bundles on hypersurfaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {1215--1221},
publisher = {Elsevier},
volume = {356},
number = {11-12},
year = {2018},
doi = {10.1016/j.crma.2018.10.004},
language = {en},
}
Girivaru V. Ravindra; Amit Tripathi. Remarks on higher-rank ACM bundles on hypersurfaces. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1215-1221. doi : 10.1016/j.crma.2018.10.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.10.004/
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