We show that the Segre product of a line and a smooth conic, naturally embedded in , is a smooth projective surface of tame representation type, namely all continuous families of indecomposable ACM bundles have dimension one. To our knowledge, this is the first example of smooth projective variety of this kind, besides the elliptic curve, which is of tame representation type according to Atiyah (1957).
Nous montrons que le produit dʼune droite et dʼune conique lisse, plongé dans par Segre, est une variété projective de type modéré, autrement dit quʼil nʼy a sur cette variété que des familles de dimension 1 au plus de fibrés indécomposables ACM. À notre connaissance, il sʼagit du premier exemple de variété lisse projective de type modéré, mise à part la courbe elliptique, qui est de ce type dʼaprès le travail fondamental dʼAtiyah (1957).
Accepted:
Published online:
Daniele Faenzi 1; Francesco Malaspina 2
@article{CRMATH_2013__351_9-10_371_0, author = {Daniele Faenzi and Francesco Malaspina}, title = {A smooth surface of tame representation type}, journal = {Comptes Rendus. Math\'ematique}, pages = {371--374}, publisher = {Elsevier}, volume = {351}, number = {9-10}, year = {2013}, doi = {10.1016/j.crma.2013.05.004}, language = {en}, }
Daniele Faenzi; Francesco Malaspina. A smooth surface of tame representation type. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 371-374. doi : 10.1016/j.crma.2013.05.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.05.004/
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☆ D.F. was partially supported by ANR-09-JCJC-0097-0 INTERLOW and ANR GEOLMI, F.M. was partially supported by Research Network Program GDRE-GRIFGA.
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