2012/12/08 by David Eisenbud, Robin Hartshorne, Eisenbud, David +4 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Mathematical and Theoretical Analysis #Mathematics and Applications #math.AC #math.AG #msc:13C40 #msc:13P05 #msc:14M06 #msc:14Q99
paper · pdf · doi:10.48550/arxiv.1212.1841
22 pages, one figure, hyperrefs added
arxiv created 2013/01/25 · arxiv updated 2013/01/28
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 P3 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.