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On the classification of certain geproci sets

Authors :
Chiantini, Luca
Farnik, Lucja
Favacchio, Giuseppe
Harbourne, Brian
Migliore, Juan
Szemberg, Tomasz
Szpond, Justyna
Publication Year :
2023

Abstract

In this short note we develop new methods toward the ultimate goal of classifying geproci sets in $\mathbb P^3$. We apply these methods to show that among sets of $16$ points distributed evenly on $4$ skew lines, up to projective equivalence there are only two distinct geproci sets. We give different geometric distinctions between these sets. The methods we develop here can be applied in a more general set-up; this is the context of the follow-up work arXiv:2308.00761.<br />Comment: 13 pages, to appear in the proceedings of the 2022 Workshop in Cortona: "Lefschetz Properties: Current and New Directions'

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2303.16263
Document Type :
Working Paper