We prove that a torsion-free sheaf F endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal ex- tension property admits a direct-sum decomposition F ≃ U \oplus A where U is a hermitian flat bundle and A is a generically ample sheaf. The result applies to the case of direct images of relative pluricanonical bundles f_*(\omega_{X/Y}^{\otimes m}) under a surjective morphism f : X → Y of smooth projective varieties with m ≥ 2. This extends previous results of Fujita, Catanese–Kawamata, and Iwai.
Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata / L. Lombardi, C. Schnell. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 152:1(2024), pp. 137-146. [10.1090/proc/16625]
Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata
L. Lombardi
Primo
;
2024
Abstract
We prove that a torsion-free sheaf F endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal ex- tension property admits a direct-sum decomposition F ≃ U \oplus A where U is a hermitian flat bundle and A is a generically ample sheaf. The result applies to the case of direct images of relative pluricanonical bundles f_*(\omega_{X/Y}^{\otimes m}) under a surjective morphism f : X → Y of smooth projective varieties with m ≥ 2. This extends previous results of Fujita, Catanese–Kawamata, and Iwai.File | Dimensione | Formato | |
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