The paper proves continuity of deformed mass and phase functions on stability condition spaces, deduces a homeomorphic embedding into measures, and establishes a triangle inequality plus truncation estimates.
The Kato-Nakayama space as a transcendental root stack
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abstract
We give a functorial description of the Kato-Nakayama space of a fine saturated log analytic space that is similar in spirit to the functorial description of root stacks. As a consequence we get a global description of the comparison map constructed in arXiv:1511.00037 from the Kato-Nakayama space to the (topological) infinite root stack.
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2026 1verdicts
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Properties of deformed mass and phase functions
The paper proves continuity of deformed mass and phase functions on stability condition spaces, deduces a homeomorphic embedding into measures, and establishes a triangle inequality plus truncation estimates.