Kyoto Journal of Mathematics

Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram

Kazuya Kato, Chikara Nakayama, and Sampei Usui

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We complete the construction of the fundamental diagram of various partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. The diagram includes the space of nilpotent orbits, the space of SL(2)-orbits, and the space of Borel–Serre orbits. We give amplifications of this fundamental diagram and amplify the relations of these spaces. We describe how this work is useful in understanding asymptotic behaviors of Beilinson regulators and of local height pairings in degeneration. We discuss mild degenerations in which regulators converge.

Article information

Kyoto J. Math., Volume 58, Number 2 (2018), 289-426.

Received: 2 February 2016
Accepted: 23 September 2016
First available in Project Euclid: 19 December 2017

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Zentralblatt MATH identifier

Primary: 14C30: Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
Secondary: 14D07: Variation of Hodge structures [See also 32G20] 32G20: Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]

Hodge theory moduli compactification regulator height pairing


Kato, Kazuya; Nakayama, Chikara; Usui, Sampei. Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram. Kyoto J. Math. 58 (2018), no. 2, 289--426. doi:10.1215/21562261-2017-0024.

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