Rings of tautological forms on moduli spaces of curves

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-09-01 DOI:10.1016/j.exmath.2023.02.008

Robin de Jong, Stefan van der Lugt

引用次数: 0

Abstract

We define and study a natural system of tautological rings on the moduli spaces of marked curves at the level of differential forms. We show that certain 2-forms obtained from the natural normal functions on these moduli spaces are tautological. Also we show that rings of tautological forms are always finite dimensional. Finally we characterize the Kawazumi–Zhang invariant as essentially the only smooth function on the moduli space of curves whose Levi form is a tautological form.

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曲线模空间上的同义形式环

在微分形式的水平上，在标记曲线的模空间上定义并研究了一个重言环的自然系统。我们证明了由这些模空间上的自然正规函数得到的某些2-形式是重言的。我们还证明了同义形式的环总是有限维的。最后，我们将Kawazumi-Zhang不变量定性为Levi形式为重言形式的曲线模空间上的唯一光滑函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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