Hyperelliptic A_r-stable curves (and their moduli stack)

2023/02/22 by Michele Pernice, Pernice, Michele
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2302.11456

openalex publication_date 2023/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is the second in a series of four papers aiming to describe the (almost integral) Chow ring of \Mbar₃, the moduli stack of stable curves of genus 3. In this paper, we introduce the moduli stack \Htilde_g^r of hyperelliptic A_r-stable curves and generalize the theory of hyperelliptic stable curves to hyperelliptic A_r-stable curves. In particular, we prove that \Htilde_g^r is a smooth algebraic stacks which can be described using cyclic covers of twisted curves of genus 0 and it embeds in \Mtilde_g^r (the moduli stack of A_r-stable curves) as the closure of the moduli stack of smooth hyperelliptic curves.

Related

• The moduli stack of A_r-stable curves
• A_r-stable curves and the Chow ring of M₃
• The Integral Chow Ring of the Stack of Pointed Hyperelliptic Curves
• Moduli of Curves of Genus One with Twisted Fields
• The (almost) integral Chow ring of M₃