Rings of tautological forms on moduli spaces of curves

Author(s):
Jong, R.S. de (0000-0002-6264-9994); Lugt, S. van der
Published
2023
Publication type
Article / Letter to editor

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.

Arakelov Green’s functionDeligne pairingKawazumi–Zhang invariantModuli space of curvesTautological ring
Date issued
2023
Language
English
Publisher
Elsevier BV
Is part of
Expositiones Mathematicae (2023), Vol. 41, no. 3, p. 531-565
hdl
1887/3714589
doi
10.1016/j.exmath.2023.02.008

Funding

Sponsorship
NWO
Grant number
613.001.401