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no. 3
Projectively flat log smooth pairs
Stéphane Druel1
1 Univ Lyon, CNRS, Université Claude Bernard Lyon 1, UMR 5208, Institut Camille Jordan, F-69622 Villeurbanne, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 3, pp. 611-645.

In this article, we study projective log smooth pairs with numerically flat normalized logarithmic tangent bundle. Generalizing works of Jahnke–Radloff and Greb–Kebekus–Peternell, we show that, passing to an appropriate finite cover and up to isomorphism, these are the projective spaces or the log smooth pairs with numerically flat logarithmic tangent bundles blown-up at finitely many points away from the boundary. On the other hand, the structure of log smooth pairs with numerically flat logarithmic tangent bundle is well understood: they are toric fiber bundles over finite étale quotients of abelian varieties.

Dans cet article, nous étudions les paires log lisses dont le fibré tangent logarithmique normalisé est numériquement plat. Généralisant des travaux de Jahnke–Radloff et Greb–Kebekus–Peternell, nous montrons qu’un revêtement fini convenable d’une telle paire est isomorphe à un espace projectif ou à l’éclatement en un nombre fini de points hors du bord d’une paire log lisse dont le fibré tangent logarithmique est numériquement plat. La structure de ces dernières est par ailleurs bien comprise : ce sont des fibrés en variétés toriques sur des quotients étales de variétés abéliennes par des groupes finis.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1783
Classification: 32Q30, 32Q26, 14E20, 14E30, 53B10

Stéphane Druel 1

1 Univ Lyon, CNRS, Université Claude Bernard Lyon 1, UMR 5208, Institut Camille Jordan, F-69622 Villeurbanne, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Stéphane Druel. Projectively flat log smooth pairs. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 3, pp. 611-645. doi : 10.5802/afst.1783. https://afst.centre-mersenne.org/articles/10.5802/afst.1783/

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