Rings of tautological forms on moduli spaces of curves
Algebraic Geometry
2023-05-24 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2207.05428,
title = {Rings of tautological forms on moduli spaces of curves},
author = {Robin de Jong and Stefan van der Lugt},
journal= {arXiv preprint arXiv:2207.05428},
year = {2023}
}
Comments
32 pages; v2: incorporated referee's remarks