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<p>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.</p>

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Analog of Satake–Baily–Borel for period maps

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Mark Green,
  • Phillip Griffiths,
  • Colleen Robles

摘要

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.