The Cohen-Macaulay space of twisted cubics
Abstract
In this work, we describe the Cohen-Macaulay space CM of twisted cubics parameterizing curves C together with a finite map i: C P3 that is generically a closed immersion and such that C has Hilbert polynomial p(t)=3t+1 with respect to i. We show that CM is irreducible, smooth and birational to one component of the Hilbert scheme of twisted cubics.
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