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June 2018 Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram
Kazuya Kato, Chikara Nakayama, Sampei Usui
Kyoto J. Math. 58(2): 289-426 (June 2018). DOI: 10.1215/21562261-2017-0024

Abstract

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.

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Kazuya Kato. Chikara Nakayama. Sampei Usui. "Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram." Kyoto J. Math. 58 (2) 289 - 426, June 2018. https://doi.org/10.1215/21562261-2017-0024

Information

Received: 2 February 2016; Accepted: 23 September 2016; Published: June 2018
First available in Project Euclid: 19 December 2017

zbMATH: 06896956
MathSciNet: MR3799704
Digital Object Identifier: 10.1215/21562261-2017-0024

Subjects:
Primary: 14C30
Secondary: 14D07, 32G20

Rights: Copyright © 2018 Kyoto University

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Vol.58 • No. 2 • June 2018
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