Rings of tautological forms on moduli spaces of curves

Jong, R.S. de; Lugt, S. van der (2023)

Article / Letter to editor

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.

• Arakelov Green’s function
• Deligne pairing
• Kawazumi–Zhang invariant
• Moduli space of curves
• Tautological ring

• All authors: Jong, R.S. de; Lugt, S. van der
• Date: 2023
• Journal: Expositiones Mathematicae
• Volume: 41
• Issue: 3
• Pages: 531 - 565
• DOI: doi:10.1016/j.exmath.2023.02.008
• Sponsorship: NWO
• Grant number: 613.001.401