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arXiv · 2304.11303

Classifying spaces of degenerating mixed Hodge structures, VI: Log real analytic functions and log $C^{\infty}$ functions

Kazuya Kato·Chikara Nakayama·Sampei Usui
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Abstract

To advance our log Hodge theory, we introduce log real analytic functions and log $C^{\infty}$ functions, define how to integrate them, and prove the log Poincar\'e lemma. We give better understandings of the degeneration of Hodge structure, including a geometric interpretation of the theory of $SL(2)$-orbits.

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Kazuya Kato, Chikara Nakayama, Sampei Usui. 2023-04-22. Classifying spaces of degenerating mixed Hodge structures, VI: Log real analytic functions and log $C^{\infty}$ functions. https://arxiv.org/abs/2304.11303

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