Hyperelliptic $A_r$-stable curves (and their moduli stack)

Michele Pernice

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arXiv · 2302.11456

Hyperelliptic $A_r$-stable curves (and their moduli stack)

Michele Pernice

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Abstract

This paper is the second in a series of four papers aiming to describe the (almost integral) Chow ring of $\Mbar_3$, 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.

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BibTeX RIS

Michele Pernice. 2023-02-22. Hyperelliptic $A_r$-stable curves (and their moduli stack). https://arxiv.org/abs/2302.11456

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