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- W4385889593 abstract "Let $P$ be the image of a period map. We discuss progress towards a conjectural Hodge theoretic completion $overline{P}$, an analogue of the Satake-Baily-Borel compactification in the classical case. The set $overline{P}$ is defined and given the structure of a compact Hausdorff topological space. We conjecture that it admits the structure of a compact complex analytic variety. We verify this conjecture when $mathrm{dim} P le 2$. In general, $overline{P}$ admits a finite cover $overline{S}$ (also a compact Hausdorff space, and constructed from Stein factorizations of period maps). Assuming that $overline{S}$ is a compact complex analytic variety, we show that a lift of the augmented Hodge line bundle $Lambda$ extends to an ample line bundle, giving $overline{P}$ the structure of a projective normal variety. Our arguments rely on refined positivity properties of Chern forms associated to various Hodge bundles; properties that might be of independent interest." @default.
- W4385889593 created "2023-08-17" @default.
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- W4385889593 date "2017-08-30" @default.
- W4385889593 modified "2023-10-05" @default.
- W4385889593 title "Period mappings and properties of the augmented Hodge line bundle" @default.
- W4385889593 doi "https://doi.org/10.48550/arxiv.1708.09523" @default.
- W4385889593 hasPublicationYear "2017" @default.
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