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Modular compactifications of $\mathcal M_{2,n}$ with Gorenstein singularities

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arxiv 1906.06367 v2 pith:MCJKFULA submitted 2019-06-14 math.AG

classification math.AG
keywords singularitiesgorensteinmathcalcomecompactificationsconditionconjugatecontaining
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abstract

We study the geometry of Gorenstein curve singularities of genus two, and of their stable limits. These singularities come in two families, corresponding to either Weierstrass or conjugate points on a semistable tail. For every $1\leq m <n$, a stability condition - using one of the markings as a reference point, and therefore not $\mathfrak S_n$-symmetric - defines proper Deligne-Mumford stacks $\overline{\mathcal M}_{2,n}^{(m)}$ containing the locus of smooth curves as a dense open substack.

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  1. Contractions of subcurves of families of log curves

    math.AG 2019-08 conditional novelty 7.0 of 10

    For families of log curves carrying a mesa structure, the selected subcurve can be contracted in a base-change-compatible way, yielding contractions between moduli spaces of curves.

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