Twenty Points in P^3
Algebraic Geometry
2013-01-28 v2 Commutative Algebra
Abstract
Using the possibility of computationally determining points on a finite cover of a unirational variety over a finite field, we determine all possibilities for direct Gorenstein linkages between general sets of points in P^3 over an algebraically closed field of characteristic 0. As a consequence we show that a general set of d points is glicci (that is, in the Gorenstein linkage class of a complete intersection) if d <= 33 or d=37,38. Computer algebra plays an essential role in the proof. The case of 20 points had been an outstanding problem in the area for a dozen years.
Cite
@article{arxiv.1212.1841,
title = {Twenty Points in P^3},
author = {David Eisenbud and Robin Hartshorne and Frank-Olaf Schreyer},
journal= {arXiv preprint arXiv:1212.1841},
year = {2013}
}
Comments
22 pages, one figure, hyperrefs added