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- W4313334734 abstract "The purpose of this paper is to study certain notions of metric positivity called “minimal extension property” for the lowest nonzero piece in the Hodge filtration of a Hodge module. Let X be a complex manifold and let $$mathcal {M}$$ be a polarized pure Hodge module on X with strict support X. Let $$F_pmathcal {M}$$ be the smallest nonzero piece in the Hodge filtration. Assume that $$mathcal {M}$$ is smooth outside a closed analytic subset Z and let $$j:Xsetminus Z hookrightarrow X$$ be the open embedding. Let h be the smooth hermitian metric on $$F_pmathcal {M}|_{Xsetminus Z}$$ induced by the polarization. We show that the canonical morphism of $$mathcal {O}_X$$ -modules $$begin{aligned} F_pmathcal {M}rightarrow j_{*}(F_pmathcal {M}|_{Xsetminus Z}) end{aligned}$$ induces an isomorphism between $$F_pmathcal {M}$$ and the subsheaf of $$j_{*}(F_pmathcal {M}|_{Xsetminus Z})$$ consisting of sections which are locally $$L^2$$ near Z with respect to h and the standard Lebesgue measure on X. In particular, h extends to a singular hermitian metric on $$F_pmathcal {M}$$ with minimal extension property." @default.
- W4313334734 created "2023-01-06" @default.
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- W4313334734 date "2022-12-29" @default.
- W4313334734 modified "2023-10-02" @default.
- W4313334734 title "Hodge modules and singular hermitian metrics" @default.
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- W4313334734 doi "https://doi.org/10.1007/s00209-022-03165-7" @default.
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