Abstract
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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