The one-dimensional stratum in the boundary of the moduli stack of stable curves

Details The one-dimensional stratum in the boundary of the moduli stack of stable curves The one-dimensional stratum in the boundary of the moduli stack of stable curves

2007-12-27

arxiv.org/abs/0712.4251v1

Mathematics

Algebraic Geometry

34 pages

Scientific paper

The moduli stack of Deligne-Mumford stable curves of genus g admits a stratification, so that the number of nodes of the curves belonging to one stratum is constant. The irreducible components of the stratum corresponding to curves with exactly 3g-4 nodes are one-dimensional substacks. We show how they can be related to moduli stacks of (permutation classes of) pointed stable curves. Using this, we construct all components of this stratum in a new way as quotient stacks.

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