On the structure of a log smooth pair in the equality case of the Bogomolov–Gieseker inequality
[Sur la structure d’une paire lisse logarithmique dans le cas d’égalité de l’inégalité de Bogomolov–Gieseker]
Iwai, Masataka1
1 Department of Mathematics, Graduate School of Science, Osaka University, 1-1, Machikaneyama-cho, Toyonaka, Osaka 560-0043 (Japan)
Annales de l'Institut Fourier, Online first, 17 p.

Nous étudions la structure d’une paire lisse logarithmique lorsque l’égalité tient dans l’inégalité de Bogomolov–Gieseker pour le faisceau tangent logarithmique et que ce faisceau est semistable par rapport à un certain diviseur ample. Nous étudions également le cas du sheaf d’extension canonique.

We study the structure of a log smooth pair when the equality holds in the Bogomolov–Gieseker inequality for the logarithmic tangent bundle and this bundle is semistable with respect to some ample divisor. We also study the case of the canonical extension sheaf.

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DOI : 10.5802/aif.3651
Classification : 32Q30, 14M22, 14E30, 32Q26
Keywords: Bogomolov–Gieseker inequality, Logarithmic tangent bundle, Log smooth pair, Projectively flat, Numerically projectively flat, Stability, Uniformization, Rational curve, MRC fibration, Rationally connected.
Mot clés : Inégalité de Bogomolov–Gieseker, fibré tangent logarithmique, paire lisse logarithmique, projectivement plat, numériquement projectivement plat, stabilité, uniformisation, courbe rationnelle, fibration MRC, rationnellement connexe.

Iwai, Masataka 1

1 Department of Mathematics, Graduate School of Science, Osaka University, 1-1, Machikaneyama-cho, Toyonaka, Osaka 560-0043 (Japan) 
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Iwai, Masataka. On the structure of a log smooth pair in the equality case of the Bogomolov–Gieseker inequality. Annales de l'Institut Fourier, Online first, 17 p.

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