Abstract
Let a ⊆ ℂ[x 1, …, x n ] be a monomial ideal and J (a c) the multiplier ideal of a with coefficient c. Then J (a c) is also a monomial ideal of ℂ[x 1, …, x n ], and the equality J (a c) = a implies that 0 < c < n + 1. We mainly discuss the problem when J (a) = a or \(J({a^{n = 1 - \varepsilon }}) = a\) for all 0 < ε < 1. It is proved that if J (a) = a then a is principal, and if \(J({a^{n = 1 - \varepsilon }}) = a\) holds for all 0 < ε < 1 then a = (x 1, …, x n ). One global result is also obtained. Let ã be the ideal sheaf on ℙn−1 associated with a. Then it is proved that the equality J (ã) = ã implies that ã is principal.
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Both authors are supported by the National Natural Science Foundation of China (No. 11401413 and No. 11471234).
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Gong, C., Tang, Z. A note on the multiplier ideals of monomial ideals. Czech Math J 65, 905–913 (2015). https://doi.org/10.1007/s10587-015-0216-z
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DOI: https://doi.org/10.1007/s10587-015-0216-z