Borel Degenerations of Arithmetically Cohen-Macaulay curves in P^3
Algebraic Geometry
2016-09-30 v2 Commutative Algebra
Abstract
We investigate Borel ideals on the Hilbert scheme components of arithmetically Cohen-Macaulay (ACM) codimension two schemes in P^n. We give a basic necessary criterion for a Borel ideal to be on such a component. Then considering ACM curves in P^3 on a quadric we compute in several examples all the Borel ideals on their Hilbert scheme component. Based on this we conjecture which Borel ideals are on such a component, and for a range of Borel ideals we prove that they are on the component.
Keywords
Cite
@article{arxiv.1111.2754,
title = {Borel Degenerations of Arithmetically Cohen-Macaulay curves in P^3},
author = {Gunnar Floystad and Margherita Roggero},
journal= {arXiv preprint arXiv:1111.2754},
year = {2016}
}
Comments
20 pages, shorter and more effective version