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

This paper is the second in a series of four papers aiming to describe the (almost integral) Chow ring of \overline {\mathcal {M}}_3, the moduli stack of stable curves of genus 3. In this paper, we introduce the moduli stack \widetilde {\mathcal {H}}_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 \widetilde {\mathcal {H}}_g^r is a smooth algebraic stack that can be described using cyclic covers of twisted curves of genus 0 and it embeds in \widetilde {\mathcal M}_g^r (the moduli stack of A_r-stable curves) as the closure of the moduli stack of smooth hyperelliptic curves. [ABSTRACT FROM AUTHOR]