no. 9
Algebraic geometry
On a question of Mehta and Pauly
Presented by: Claire Voisin
Brenner, Holger1; Stäbler, Axel2
1Universität Osnabrück, Fachbereich 6, Albrechtstr. 28a, 49069 Osnabrück, Germany
2Johannes Gutenberg-Universität Mainz, Fachbereich 8, Staudingerweg 9, 55099 Mainz, Germany
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 F⁎E 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 F⁎E 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 
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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

[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

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