Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 58, Number 2 (2018), 289-426.
Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram
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 -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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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. https://projecteuclid.org/euclid.kjm/1513674221