Holomorphic maps between moduli spaces II

TL;DR

This paper proves that under certain genus conditions, the only non-constant holomorphic maps between specific moduli spaces are forgetful maps, establishing a uniqueness result in complex geometry.

Contribution

It demonstrates that for genus g ≥ 4, the only non-constant holomorphic maps between moduli spaces are forgetful maps, under a specific genus bound.

Findings

Forgetful maps are the only non-constant holomorphic maps under given conditions.

The result applies for g ≥ 4 and g' ≤ 3·2^{g-3}.

Provides a classification of holomorphic maps between these moduli spaces.

Abstract

We prove that forgetful maps are the only non-constant holomorphic maps $\mathcal{M}_{g,r}\to \mathcal{M}_{g',r'}$ between moduli spaces, as long as $g\ge 4$ and $g'\le 3\cdot 2^{g-3}$.