Algebraic geometry
On a question of Mehta and Pauly
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 855-857.

In this short note, we provide explicit examples in characteristic p on certain smooth projective curves where for a given semistable vector bundle E the length of the Harder–Narasimhan filtration of FE is longer than p. This negatively answers a question of Mehta and Pauly raised in [2].

Dans cette courte note, nous donnons des exemples explicites en caracteristique p sur certaines courbes projectives lisses où, pour un fibré vectoriel semi-stable donné E, la longeur de la filtration d'Harder–Narasimhan de FE est plus grande que p. Cela répond negativement à une question posée par Mehta et Pauly dans [2].

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.06.007
Brenner, Holger 1; Stäbler, Axel 2

1 Universität Osnabrück, Fachbereich 6, Albrechtstr. 28a, 49069 Osnabrück, Germany
2 Johannes Gutenberg-Universität Mainz, Fachbereich 8, Staudingerweg 9, 55099 Mainz, Germany
@article{CRMATH_2015__353_9_855_0,
     author = {Brenner, Holger and St\"abler, Axel},
     title = {On a question of {Mehta} and {Pauly}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {855--857},
     publisher = {Elsevier},
     volume = {353},
     number = {9},
     year = {2015},
     doi = {10.1016/j.crma.2015.06.007},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2015.06.007/}
}
TY  - JOUR
AU  - Brenner, Holger
AU  - Stäbler, Axel
TI  - On a question of Mehta and Pauly
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 855
EP  - 857
VL  - 353
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2015.06.007/
DO  - 10.1016/j.crma.2015.06.007
LA  - en
ID  - CRMATH_2015__353_9_855_0
ER  - 
%0 Journal Article
%A Brenner, Holger
%A Stäbler, Axel
%T On a question of Mehta and Pauly
%J Comptes Rendus. Mathématique
%D 2015
%P 855-857
%V 353
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2015.06.007/
%R 10.1016/j.crma.2015.06.007
%G en
%F CRMATH_2015__353_9_855_0
Brenner, Holger; Stäbler, Axel. On a question of Mehta and Pauly. Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 855-857. doi : 10.1016/j.crma.2015.06.007. http://www.numdam.org/articles/10.1016/j.crma.2015.06.007/

[1] Lange, H.; Pauly, C. On Frobenius-destabilized rank-2 vector bundles over curves, Comment. Math. Helv., Volume 83 (2008), pp. 179-209

[2] Mehta, V.B.; Pauly, C. Semistability of Frobenius direct images over curves, Bull. Soc. Math. Fr., Volume 135 (2007) no. 1, pp. 105-117

[3] Sun, X. Direct images of bundles under Frobenius morphism, Invent. Math., Volume 173 (2008) no. 173, pp. 427-447

[4] Zhou, M. The H-N filtration of bundles as Frobenius pull-back, 2012 (preprint) | arXiv

Cited by Sources: