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3 results for “Kawazumi-Zhang”

A twisted invariant of a compact Riemann surfacemath.GT

New invariant for Riemann surfaces connects to moduli space classes.

problem Understanding Riemann surface invariants and their relationships.

method Introducing a twisted version of the Kawazumi-Zhang invariant and relating it to other classes.

result The new invariant connects to the first Mumford-Morita-Milller class on the moduli space.

Riemann surface invariant moduli space Kawazumi-Zhang Mumford-Morita-Milller

2022-10-02abs ↗pdf ↗

Asymptotic behavior of the Kawazumi-Zhang invariant for degenerating Riemann surfacesmath.AG

Around 2008 N. Kawazumi and S. Zhang introduced a new fundamental numerical invariant for compact Riemann surfaces. One way of viewing the Kawazumi-Zhang invariant is as a quotient of two natural hermitian metrics with the same first Chern form on the line bundle of holomorphic differentials. In this paper we determine…

2012-07-10abs ↗pdf ↗

Rings of tautological forms on moduli spaces of curvesmath.AG

Study of tautological forms on curve moduli spaces.

problem Understanding tautological forms on moduli spaces of curves.

method Defined and studied a system of tautological rings on moduli spaces of marked curves, showing certain 2-forms are tautological and rings are finite dimensional.

result Characterized the Kawazumi-Zhang invariant as a tautological form.

tautological forms moduli spaces curves differential forms finite dimensional

2022-07-12abs ↗pdf ↗