Moduli spaces of hyperelliptic curves with A and D singularities
Tóm tắt
We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two rational parameters describing allowable singularities. For the extreme values of the parameters, we obtain the stacks of stable limits of
$$A_n$$
and
$$D_n$$
singularities, and the quotients of the miniversal deformation spaces of these singularities by natural
$$\mathbb G _m$$
-actions. We interpret the intermediate spaces as log canonical models of the stacks of stable limits of
$$A_n$$
and
$$D_n$$
singularities.
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