论文标题
曲线模量空间上的重言式形式的环
Rings of tautological forms on moduli spaces of curves
论文作者
论文摘要
我们在差异形式的水平上定义并研究了在标记曲线的模量空间上进行重言式环的自然系统。我们表明，从这些模量空间上的天然正常功能获得的某些2形是重言式学。我们还表明，重言式形式的环总是有限的维度。最后，我们将Kawazumi-Zhang不变性表征为本质上是曲线模量空间上唯一的平滑函数，其曲线形式是一种重言式形式。
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.
