부산대학교 도서관

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.
Comment: The paper is one of the four papers that compose the author's PhD thesis. In particular, it contains Section 1.1, Section 1.3 and Section 1.4 of arXiv:2211.09793. Some typos have been corrected and the exposition was improved. 35 pages; comments are very welcome