The space of Cohen-Macaulay curves

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.

39 pages

References in corpus (1)

• Curve counting via stable pairs in the derived category

Cited by in corpus (1)

• The Cohen-Macaulay space of twisted cubics