Analog of Satake-Baily-Borel for period maps
Algebraic Geometry
2025-04-08 v6
Abstract
We propose an analog of the Satake--Baily--Borel compactification and Borel's extension theorem for arbitrary period maps. The proposed analog is constructed as a proper topological completion of the period map. It is conjectured that the construction is projective algebraic, and the conjecture is reduced to a certain extension problem.
Keywords
Cite
@article{arxiv.2010.06720,
title = {Analog of Satake-Baily-Borel for period maps},
author = {Mark Green and Phillip Griffiths and Colleen Robles},
journal= {arXiv preprint arXiv:2010.06720},
year = {2025}
}
Comments
This is a major revision. The previous version has been separated into two parts; this is Part 1. The previous version erroneously claimed that certain line bundles $\mathrm{det}(F^p)$ descend to the SBB completion. We thank Ben Bakker for providing a counter-example. We are able to show that the product $\prod_p\,\mathrm{det}(F^p)^{\otimes m_p}$ descends, for suitable choice of $m_p > 0$