Geproci sets on skew lines in $\mathbb P^3$ with two transversals

Luca Chiantini; Pietro De Poi; Lucja Farnik; Giuseppe Favacchio; Brian Harbourne; Giovanna Ilardi; Juan Migliore; Tomasz Szemberg; Justyna Szpond

arXiv · 2312.04644

Geproci sets on skew lines in $\mathbb P^3$ with two transversals

Luca Chiantini·Pietro De Poi·Lucja Farnik·Giuseppe Favacchio·Brian Harbourne·Giovanna Ilardi·Juan Migliore·Tomasz Szemberg·Justyna Szpond

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Abstract

The purpose of this work is to pursue classification of geproci sets. Specifically we classify $[m,n]$-geproci sets which consist of $m=4$ points on each of $n$ skew lines, assuming the skew lines have two transversals in common. We show that in this case $n\leq 6$. Moreover we show that all geproci sets of this type are contained in the \emph{standard construction} for $m=4$ introduced in arXiv:2209.04820. Finally, we propose a conjectural representation for all geproci sets of this type, irrespective of the number $m$ of points on each skew line.

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Luca Chiantini, Pietro De Poi, Lucja Farnik, Giuseppe Favacchio, Brian Harbourne, Giovanna Ilardi, Juan Migliore, Tomasz Szemberg, Justyna Szpond. 2023-12-07. Geproci sets on skew lines in $\mathbb P^3$ with two transversals. https://arxiv.org/abs/2312.04644

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