Abstract
We consider two simplicial arrangements of lines and ideals of intersection points of these lines. There are intersection points in both cases and the numbers of points lying on exactly configuration lines (points of multiplicity ) coincide. We show that in one of these examples the containment holds, whereas it fails in the other. We also show that the containment fails for a subarrangement of lines. The interest in the containment relation between and for ideals of points in is motivated by a question posted by Hochster and Huneke in . Configurations of points with are quite rare. Our example reveals two particular features: All points are defined over and all intersection points of lines are involved. In examples studied by now only points with multiplicity were considered. The novelty of our arrangements lies in the geometry of the element in which witness the noncontainment in . In all previous examples such an element was a product of linear forms. Now, in both cases there is an irreducible curve of higher degree involved.
Citation
Marek Janasz. Magdalena Lampa-Baczyńska. Grzegorz Malara. "New phenomena in the containment problem for simplicial arrangements." J. Commut. Algebra 14 (4) 571 - 581, Winter 2022. https://doi.org/10.1216/jca.2022.14.571
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