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

Zhongming Tang () and Cheng Gong ()
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Zhongming Tang: Soochow (Suzhou) University
Cheng Gong: Soochow (Suzhou) University

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 2, 167-176

Abstract: Abstract 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] $$\widetilde {\mathcal{J}\left( a \right)}$$ J ( a ) ˜ on ℙ d–1 associated to J (a) that H i(ℙ d–1; $$\widetilde {\mathcal{J}\left( a \right)}$$ J ( a ) ˜ (s–i)) = 0, for all i > 0 and s ≥ d(a).

Keywords: Stability; Castelnuovo-Mumford regularity; multiplier ideals (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0217-8

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