A closer look at the stacks of stable pointed curves

Details A closer look at the stacks of stable pointed curves A closer look at the stacks of stable pointed curves

2011-06-08

arxiv.org/abs/1106.1588v2

Mathematics

Algebraic Geometry

17 pages

Scientific paper

10.1016/j.jpaa.2012.03.21

In the theory of the moduli-stacks of n-pointed stable curves, there are two fundamental functors, contraction and stabilization. These functors are constructed in [4], where they are used to show that the various \bar{M_{g,n}}'s are DM-stacks. We give here a more elementary and more complete proof of the fact that stabilization, as it is de?fined in [4], is a functor. The fact that contraction is a functor inverse to the stabilization-functor we think is satisfactorily treated in [4]. In a very recent publication [1] there is a proof based on the proof in [4], but it is adapted to the case of moduli stacks over the complex numbers. In this note we work in the most general setting, i.e. over the integers.

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