## Katharina Heinrich ; Roy Skjelnes ; Jan Stevens - The space of twisted cubics

epiga:5573 - Épijournal de Géométrie Algébrique, June 3, 2021, Volume 5 - https://doi.org/10.46298/epiga.2021.volume5.5573
The space of twisted cubics

Authors: Katharina Heinrich ; Roy Skjelnes ; Jan Stevens

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.

Volume: Volume 5
Published on: June 3, 2021
Accepted on: March 5, 2021
Submitted on: June 13, 2019
Keywords: Mathematics - Algebraic Geometry,14C05, 14D22, 14H10, 14A20