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— We study singularities of the Narasimhan-Simha Hermitian metric on the direct image of a relative pluricanonical bundle. The upper bound relates to log-canonical thresholds. Résumé. — Nous étudions les singularités des métriques hermitiennes de NarasimhanSimha sur les images directes des fibrés pluricanoniques relatifs. La majoration est liée aux seuils log-canoniques.

Singularities of Narasimhan-Simha type metrics on direct images of relative pluricanonical bundles