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We introduce a twisted version of the Kawazumi–Zhang invariant \(a_g(C) = \varphi (C)\) of a compact Riemann surface C of genus \(g \geq 1\) , and discuss how it is related to the first Mumford–Morita–Milller class \(e_1 = \kappa _1\) on the moduli space of compact Riemann surfaces and the original Kawazumi–Zhang invariant.

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A Twisted Invariant of a Compact Riemann Surface

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  • 发表日期：

    2025年

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  • Nariya Kawazumi

摘要

We introduce a twisted version of the Kawazumi–Zhang invariant \(a_g(C) = \varphi (C)\) of a compact Riemann surface C of genus \(g \geq 1\) , and discuss how it is related to the first Mumford–Morita–Milller class \(e_1 = \kappa _1\) on the moduli space of compact Riemann surfaces and the original Kawazumi–Zhang invariant.