Asian Journal of Mathematics

Volume 18 (2014)

Number 4

Boundaries of cycle spaces and degenerating Hodge structures

Pages: 687 – 706

DOI: https://dx.doi.org/10.4310/AJM.2014.v18.n4.a6

Author

Tatsuki Hayama (Department of Mathematics, National Taiwan University, Taipei, Taiwan; and Mathematical Sciences Center, Tsinghua University, Beijing, China)

Abstract

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 $h^{2,1} = 1$.

Keywords

degenerating Hodge structure, partial compactification of period domain, cycle space

2010 Mathematics Subject Classification

14D07, 32G20

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Published 4 November 2014