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• W2892066585 startingPage "106435" @default.
• W2892066585 abstract "The symbolic powers I(n) of a radical ideal I in a polynomial ring consist of the functions that vanish up to order n in the variety defined by I. These do not necessarily coincide with the ordinary algebraic powers In, but it is natural to compare the two notions. The containment problem consists of determining the values of n and m for which I(n)⊆Im holds. When I is an ideal of height 2 in a regular ring, I(3)⊆I2 may fail, but we show that this containment does hold for the defining ideal of the space monomial curves (ta,tb,tc). More generally, given a radical ideal I of big height h, while the containment I(hn−h+1)⊆In conjectured by Harbourne does not necessarily hold for all n, we give sufficient conditions to guarantee I(hn−h+1)⊆In for n≫0." @default.
• W2892066585 created "2018-09-27" @default.
• W2892066585 creator A5024192935 @default.
• W2892066585 date "2020-12-01" @default.
• W2892066585 modified "2023-09-29" @default.
• W2892066585 title "A stable version of Harbourne's Conjecture and the containment problem for space monomial curves" @default.
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• W2892066585 doi "https://doi.org/10.1016/j.jpaa.2020.106435" @default.
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