The purpose of this work is to pursue classification of geproci sets. Specifically we classify [m,n]-geproci sets Z which consist of m=4 points on each of n skew lines, assuming the skew lines have two transversals in common. We show in this case that n≤6. Moreover we show that all geproci sets of this type and with no points on the transversals are contained in the F4 configuration. We conjecture that a similar result is true for an arbitrary number m of points on each skew line, replacing containment in F4 by containment in a half grid obtained by the so-called standard construction.
Chiantini L., De Poi P., Farnik L., Favacchio G., Harbourne B., Ilardi G., et al. (2025). Geproci sets on skew lines in P3 with two transversals. JOURNAL OF PURE AND APPLIED ALGEBRA, 229(1) [10.1016/j.jpaa.2024.107809].
Geproci sets on skew lines in P3 with two transversals
Favacchio G.;
2025-01-01
Abstract
The purpose of this work is to pursue classification of geproci sets. Specifically we classify [m,n]-geproci sets Z which consist of m=4 points on each of n skew lines, assuming the skew lines have two transversals in common. We show in this case that n≤6. Moreover we show that all geproci sets of this type and with no points on the transversals are contained in the F4 configuration. We conjecture that a similar result is true for an arbitrary number m of points on each skew line, replacing containment in F4 by containment in a half grid obtained by the so-called standard construction.
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