Borel Degenerations of Arithmetically Cohen-Macaulay curves in P^3

Details Borel Degenerations of Arithmetically Cohen-Macaulay curves in P^3 Borel Degenerations of Arithmetically Cohen-Macaulay curves in P^3

2011-11-11

arxiv.org/abs/1111.2754v1

Mathematics

Algebraic Geometry

30 pages

Scientific paper

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.

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