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As a geometric application of polarized log Hodge structures, we show the following. Let M sm H be a projective variety which is a compactification of the coarse moduli space of surfaces of general type constructed by Kawamata, Kollár, Shepherd-Barron, Alexeev, Mori, Karu, et al., and let Γ\D Σ be a log manifold which is the fine moduli space of polarized log Hodge structures constructed by Kato and Usui. If we take a suitable finite cover M → M i of any irreducible component M i of M sm H , and if we assume the existence of a suitable fan Σ, then there is an extended period map ψ : M → Γ\D Σ and its image is the analytic subspace associated to a separated compact algebraic space. The point is that, although Γ\D Σ is a "log manifold" with slits, the image ψ(M ) is not affected by these slits and is a classical familiar object: a separated compact algebraic space.

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𝑆𝐿(2)-orbit theorem for degeneration of mixed Hodge structure

Katô

2007

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Cattani, Kaplan and Schmid (1986) established the SL(2)-orbit theorem in several variables for the degeneration of polarized Hodge structure. The aim of the present paper is to generalize it for the degeneration of mixed Hodge structure whose graded quotients by the weight filtration are polarized. As an application, we obtain a mixed Hodge version of an estimate of the Hodge metric for the degeneration of polarized Hodge structure.

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Cited by 9 publications

References 12 publications

Analytic Log Picard Varieties

Analytic Log Picard Varieties

Images of extended period maps

𝑆𝐿(2)-orbit theorem for degeneration of mixed Hodge structure

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