On the coherence of the $L^2$ subsheaf for a singular Hermitian metric whose determinant has analytic singularities
[Sur la cohérence du sous-faisceau $L^2$ pour une métrique hermitienne singulière dont le déterminant a des singularités analytiques]
Zou, Yongpan1
1Graduate School, of Mathematical Science, The University of Tokyo, 3-8-1 Komaba, Meguro-Ku, Tokyo 153-8914 (Japan)
Annales de l'Institut Fourier, Online first, 16 p.

We study the sheaf of the locally square integrable holomorphic section of a vector bundle with semi-positive curved singular Hermitian metric. We confirm the coherence when its induced determinant metric has analytic singularities.

Nous étudions le faisceau des sections holomorphes localement à carré intégrable d’un fibré vectoriel avec une métrique hermitienne singulière à courbure semi-positive. Nous confirmons la cohérence lorsque la métrique déterminante induite présente des singularités analytiques.

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Révisé le :
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DOI : 10.5802/aif.3782
Classification : 32L10
Keywords: coherent analytic sheaves, singular Hermitian metric, Griffiths positive
Mots-clés : faisceaux analytiques cohérents, métrique hermitienne singulière, positif au sens de Griffiths

Zou, Yongpan  1

1 Graduate School, of Mathematical Science, The University of Tokyo, 3-8-1 Komaba, Meguro-Ku, Tokyo 153-8914 (Japan) 
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Zou, Yongpan. On the coherence of the $L^2$ subsheaf for a singular Hermitian metric whose determinant has analytic singularities. Annales de l'Institut Fourier, Online first, 16 p.

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