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arXiv · 2306.06387

Asymptotic Behavior of the Zhang--Kawazumi's phi-invariant

Yinchong Song
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Abstract

The phi-invariant was introduced by Shou-Wu Zhang and Nariya Kawazumi. We study the continuity property of the phi-invariants for degenerating graphs, and show that this continuity property induces an adelic divisor on the moduli space of Riemann surfaces, and then give an asymptotic expression of the Zhang--Kawazumi's invariants for Riemann surfaces near the boundary of the moduli space. We mainly use Yuan--Zhang's adelic divisors, and follow Yuan's idea of globalization of phi-invariants.

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Yinchong Song. 2023-06-10. Asymptotic Behavior of the Zhang--Kawazumi's phi-invariant. https://doi.org/10.1016/j.aim.2023.109349

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