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- W2904780027 abstract "We consider two simplicial arrangements of lines and ideals I of intersection points of these lines. There are 127 intersection points in both cases and the numbers ti of points lying on exactly i configuration lines (points of multiplicity i) coincide. We show that in one of these examples the containment I(3)⊆I2 holds, whereas it fails in the other. We also show that the containment fails for a subarrangement of 21 lines. The interest in the containment relation between I(3) and I2 for ideals of points in ℙ2 is motivated by a question posted by Hochster and Huneke in 2002. Configurations of points with I(3)⊈I2 are quite rare. Our example reveals two particular features: All points are defined over ℚ and all intersection points of lines are involved. In examples studied by now only points with multiplicity i≥3 were considered. The novelty of our arrangements lies in the geometry of the element in I(3) which witness the noncontainment in I2. 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." @default.
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- W2904780027 date "2022-12-01" @default.
- W2904780027 modified "2023-09-23" @default.
- W2904780027 title "New phenomena in the containment problem for simplicial arrangements" @default.
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- W2904780027 doi "https://doi.org/10.1216/jca.2022.14.571" @default.
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