Moduli spaces of hyperelliptic curves with A and D singularities

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 parameters describing allowable singularities. By varying these parameters, we interpolate between the stacks of stable limits of A and D singularities and the quotients of the versal deformation spaces of A and D singularities by a natural ${\mathbb{G}}_m$ action.

Section 7 expanded. Typos and minor errors fixed. 35 pages, 2 TikZ figures

References in corpus (5)

• Log minimal model program for the moduli space of stable curves: The first flip
• Representability of Hilbert schemes and Hilbert stacks of points
• Weakly proper moduli stacks of curves
• Linear sections of the Severi variety and moduli of curves
• Moduli spaces of weighted stable curves and log canonical models of ${\bar{M}}_{g,n}$

Cited by in corpus (3)

• Alternate Compactifications of Moduli Spaces of Curves
• Weakly proper moduli stacks of curves
• The final log canonical model of the moduli space of stable curves of genus four