Rings of tautological forms on moduli spaces of curves

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.

32 pages; v2: incorporated referee's remarks

References in corpus (3)

• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Johnson's homomorphisms and the Arakelov-Green function
• Relations among tautological classes revisited