Geodesic
The space of twisted cubics
Épijournal de Géométrie Algébrique, Tome 5 (2021)

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We consider the Cohen-Macaulay compactification of the space of twisted cubics in projective n-space. This compactification is the fine moduli scheme representing the functor of CM-curves with Hilbert polynomial 3t+1. We show that the moduli scheme of CM-curves in projective 3-space is isomorphic to the twisted cubic component of the Hilbert scheme. We also describe the compactification for twisted cubics in n-space. 
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     author = {Heinrich, Katharina and Skjelnes, Roy and Stevens, Jan},
     title = {The space of twisted cubics},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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Heinrich, Katharina; Skjelnes, Roy; Stevens, Jan. The space of twisted cubics. Épijournal de Géométrie Algébrique, Tome 5 (2021). doi: 10.46298/epiga.2021.volume5.5573

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