Moduli spaces of hyperelliptic curves with A and D singularities

Details Moduli spaces of hyperelliptic curves with A and D singularities Moduli spaces of hyperelliptic curves with A and D singularities

2010-07-27

arxiv.org/abs/1007.4828v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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