[Une surface lisse de type de représentation modéré]
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).
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).
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@article{CRMATH_2013__351_9-10_371_0,
author = {Faenzi, Daniele and Malaspina, Francesco},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.05.004/}
}
TY - JOUR AU - Faenzi, Daniele AU - Malaspina, Francesco TI - A smooth surface of tame representation type JO - Comptes Rendus. Mathématique PY - 2013 SP - 371 EP - 374 VL - 351 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.05.004/ DO - 10.1016/j.crma.2013.05.004 LA - en ID - CRMATH_2013__351_9-10_371_0 ER -
%0 Journal Article %A Faenzi, Daniele %A Malaspina, Francesco %T A smooth surface of tame representation type %J Comptes Rendus. Mathématique %D 2013 %P 371-374 %V 351 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.05.004/ %R 10.1016/j.crma.2013.05.004 %G en %F CRMATH_2013__351_9-10_371_0
Faenzi, Daniele; Malaspina, Francesco. A smooth surface of tame representation type. Comptes Rendus. Mathématique, Tome 351 (2013) no. 9-10, pp. 371-374. doi : 10.1016/j.crma.2013.05.004. http://www.numdam.org/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.
