On the stability and regularity of the multiplier ideals of monomial ideals

Let a ⊆ ℂ[ x 1 , . . . , x d ] be a monomial ideal and J (a) its multiplier ideal which is also a monomial ideal. It is proved that if a is strongly stable or squarefree strongly stable then so is J (a). Denote the maximal degree of minimal generators of a by d (a). When a is strongly stable or squa...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2017-06, Vol.48 (2), p.167-176
Main Authors: Tang, Zhongming, Gong, Cheng
Format: Article
Language:English
Subjects:
Applications of Mathematics
Generators
Mathematics
Mathematics and Statistics
Numerical Analysis
Regularity
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Summary:Let a ⊆ ℂ[ x 1 , . . . , x d ] be a monomial ideal and J (a) its multiplier ideal which is also a monomial ideal. It is proved that if a is strongly stable or squarefree strongly stable then so is J (a). Denote the maximal degree of minimal generators of a by d (a). When a is strongly stable or squarefree strongly stable, it is shown that the Castelnuovo-Mumford regularity of J (a) is less than or equal to d (a). As a corollary, one gets a vanishing result on the ideal sheaf] J ( a ) ˜ on ℙ d –1 associated to J (a) that H i (ℙ d –1 ; J ( a ) ˜ ( s – i )) = 0, for all i > 0 and s ≥ d (a).
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-017-0217-8