論文

We study a property of cycle spaces in connection with degenerating Hodge structures of odd-weight, and we construct maps from some partial compactifications of period domains to the Satake compatifications of Siegel spaces. These maps are a generalization of the maps from the toroidal compactifications of Siegel spaces to the Satake compactifications. We also show continuity of these maps for the case for the Hodge structure of Calabi-Yau threefolds with h(2,1) = 1.

A flag domain is an open real group orbit in a complex flag manifold. It has been shown that a flag domain is either pseudoconvex or pseudoconcave. Moreover, generically 1-connected flag domains are pseudoconcave. In this study, for flag domains contained in irreducible Hermitian symmetric spaces of type AIII or CI, we determine which pseudoconcave flag domain is generically 1-connected.

We construct fans which give Kato-Usui partial compactifications of period domains of weight -1. Similarly to the fans of toroidal compactifications, these fans are given by polyhedral decompositions. We also demonstrate a fibration structure for some kinds of Kato-Usui boundary components.

For a variation of Hodge structure over a punctured disk, Green, Griffiths and Kerr introduced a Neron model which is a Hausdorff space that includes values of admissible normal functions. On the other hand, Kato, Nakayama and Usui introduced a Neron model as a logarithmic manifold using log mixed Hodge theory. This work constructs a homeomorphism between these two models.

In this paper, we determine when a natural torsor arising in the work of Kato and Usui on partial compactification of period domains of pure Hodge structure is trivial, and we give an application to cycle spaces.

This paper examines the moduli spaces of log Hodge structures introduced by Kato and Usui. This moduli space is a partial compactification of a discrete quotient of a period domain. This paper treats the following two cases: (A) where the period domain is Hermitian symmetric, and (B) where, the Hodge structures are of the mirror quintic type. Especially it addresses a property of the torsor.

We construct a hermitian metric on the classifying spaces of graded-polarized mixed Hodge structures and prove analogs of the strong distance estimate [6] between an admissible period map and the approximating nilpotent orbit. We also consider the asymptotic behavior of the biextension metric introduced by Hain [12], analogs of the norm estimates of [19] and the asymptotics of the naive limit Hodge filtration considered in [21]. (C) 2014 Elsevier Inc. All rights reserved.