We consider in this paper the following questions: does the Jacobian ideal of a smooth hypersurface have the Weak Lefschetz Property? Does the Jacobian ideal of a smooth hypersurface have the Strong Lefschetz Property? We prove that if X is a hypersurface in Pn of degree d>2, such that its singular locus has dimension at most n−3, then the ideal J(X) has the WLP in degree d−2. Moreover we show that if X is a hypersurface in Pn of degree d>2, such that its singular locus has dimension at most n−3, then for every positive integer k
Jacobians ideals, arrangements and the Lefschetz properties / Ilardi, Giovanna. - In: JOURNAL OF ALGEBRA. - ISSN 1090-266X. - 508:(2018), pp. 418-430. [10.1016/j.jalgebra.2018.04.029]
Jacobians ideals, arrangements and the Lefschetz properties
Giovanna Ilardi
2018
Abstract
We consider in this paper the following questions: does the Jacobian ideal of a smooth hypersurface have the Weak Lefschetz Property? Does the Jacobian ideal of a smooth hypersurface have the Strong Lefschetz Property? We prove that if X is a hypersurface in Pn of degree d>2, such that its singular locus has dimension at most n−3, then the ideal J(X) has the WLP in degree d−2. Moreover we show that if X is a hypersurface in Pn of degree d>2, such that its singular locus has dimension at most n−3, then for every positive integer k| File | Dimensione | Formato | |
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