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arXiv · 1403.6082

The space of Cohen-Macaulay curves

Katharina Heinrich
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Abstract

One can consider the Hilbert scheme as a natural compactification of the space of smooth projective curves with fixed Hilbert polynomial. Here we consider a different modular compactification, namely the functor CM parameterizing curves together with a finite map to $\mathbb{P}^n$ that is generically a closed immersion. We prove that CM is an algebraic space by contructing a scheme W and a representable, surjective and smooth map W -> CM. Moreover, we show that CM satisfies the valuative criterion for properness.

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Katharina Heinrich. 2014-03-24. The space of Cohen-Macaulay curves. https://arxiv.org/abs/1403.6082

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