Connectedness of the moduli space of all reduced curves

TL;DR

This paper proves that the moduli stack of all reduced n-pointed algebraic curves of fixed genus is connected, using advanced theories of moduli and territories.

Contribution

It introduces a novel proof of connectedness for the moduli space of reduced pointed curves based on equinormalized curves and Ishii's territories theory.

Findings

The moduli stack of all reduced n-pointed algebraic curves of fixed genus is connected.

The proof employs moduli of equinormalized curves and Ishii's territories theory.

This work advances understanding of the structure of algebraic curve moduli spaces.

Abstract

Using moduli of equinormalized curves and Ishii's theory of territories, we prove that the moduli stack of all reduced n-pointed algebraic curves of fixed arithmetic genus is connected.