The space of Cohen–Macaulay curves
(English)Manuscript (preprint) (Other academic)
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 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.
Algebra and Logic Geometry
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-143875OAI: oai:DiVA.org:kth-143875DiVA: diva2:709959
QS 20142014-04-032014-04-012014-04-04Bibliographically approved