The Cohen-Macaulay space of twisted cubics

Katharina Heinrich

The Cohen-Macaulay space of twisted cubics

Algebraic Geometry 2014-03-26 v1

Authors: Katharina Heinrich

Abstract

In this work, we describe the Cohen-Macaulay space CM of twisted cubics parameterizing curves $C$ together with a finite map $i: C \to \mathbb{P}^3$ 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.

Keywords

Cohen-Macaulay space twisted cubics Hilbert scheme parameterization birational geometry

Cite

@article{arxiv.1403.6441,
  title  = {The Cohen-Macaulay space of twisted cubics},
  author = {Katharina Heinrich},
  journal= {arXiv preprint arXiv:1403.6441},
  year   = {2014}
}

Comments

16 pages, 2 figures

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