1,720,989 research outputs found
Monomial ideals and the failure of the Strong Lefschetz property
No full textWe give a sharp lower bound for the Hilbert function in degree d of artinian quotients k[x1,…,xn]/I failing the Strong Lefschetz property, where I is a monomial ideal generated in degree d≥2. We also provide sharp lower bounds for other classes of ideals, and connect our result to the classification of the Hilbert functions forcing the Strong Lefschetz property by Zanello and Zylinski.</p
Hilbert functions of Artinian Gorenstein algebras with the strong Lefschetz property
No full textWe prove that a sequence h of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property if and only if it is an SI-sequence. This generalizes the result by T. Harima which characterizes the Hilbert functions of Artinian Gorenstein algebras with the weak Lefschetz property. We also provide classes of Artinian Gorenstein algebras obtained from the ideal of points in such that some of their higher Hessians have non-vanishing determinants. Consequently, we provide families of such algebras satisfying the SLP.QC 20200821</p
Jordan types with small parts for Artinian Gorenstein algebras of codimension three
No full textWe study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that represent the ranks of multiplication maps in various degrees. We show that there is a 1-1 correspondence between rank matrices and Jordan degree types. For Artinian Gorenstein algebras with codimension three we classify all rank matrices that occur for linear forms with vanishing third power. As a consequence, we show for such algebras that the possible Jordan types with parts of length at most four are uniquely determined by at most three parameters.QC 20200821</p
Hilbert functions of Artinian Gorenstein algebras with the strong Lefschetz property [Elektronisk resurs]
No full textWe prove that a sequence h of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property if and only if it is an SI-sequence. This generalizes the result by T. Harima which characterizes the Hilbert functions of Artinian Gorenstein algebras with the weak Lefschetz property. We also provide classes of Artinian Gorenstein algebras obtained from the ideal of points in such that some of their higher Hessians have non-vanishing determinants. Consequently, we provide families of such algebras satisfying the SLP.</p
The Weak Lefschetz Property of Equigenerated Monomial Ideals
No full textWe determine the sharp lower bound for the Hilbert function in degree d of a monomial algebra failing the WLP over a polynomial ring with n variables and generated in degree d. We consider artinian ideals in the polynomial ring with n variables generated by homogeneous polynomials of degree d invariant under an action of the cyclic group Z/dZ. We give a complete classification of such ideals in terms of the WLP depending on the action.QC 20180220</p
Jordan types with small parts for Artinian Gorenstein algebras of codimension three
No full textWe study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that represent the ranks of multiplication maps in various degrees. We show that there is a 1-1 correspondence between rank matrices and Jordan degree types. For Artinian Gorenstein algebras with codimension three we classify all rank matrices that occur for linear forms with vanishing third power. As a consequence, we show for such algebras that the possible Jordan types with parts of length at most four are uniquely determined by at most three parameters.QC 20200821</p
Hilbert Functions Of Artinian Gorenstein Algebras With The Strong Lefschetz Property
No full textWe prove that a sequence h of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property (SLP) if and only if it is an Stanley-Iarrobino-sequence. This generalizes the result by T. Harima which characterizes the Hilbert functions of Artinian Gorenstein algebras with the weak Lefschetz property. We also provide classes of Artinian Gorenstein algebras obtained from the ideal of points in P-n such that some of their higher Hessians have non-vanishing determinants. Consequently, we provide families of such algebras satisfying the SLP.</p
Lefschetz Properties of Monomial Ideals with Almost Linear Resolution
No full textWe study the WLP and SLP of artinian monomial ideals in S = K[x1, . . . , xn] via studying their minimal free resolutions. We study the Lefschetz properties of such ideals where the minimal free resolution of S/I is linear for at least n − 2 steps. We give an affirmative answer to a conjecture of Eisenbud, Huneke and Ulrich for artinian monomial ideals with almost linear resolutions.QC 20180220</p
The Weak Lefschetz Property of Equigenerated Monomial Ideals
No full textWe determine the sharp lower bound for the Hilbert function in degree d of a monomial algebra failing the WLP over a polynomial ring with n variables and generated in degree d. We consider artinian ideals in the polynomial ring with n variables generated by homogeneous polynomials of degree d invariant under an action of the cyclic group Z/dZ. We give a complete classification of such ideals in terms of the WLP depending on the action.QC 20180220</p
Lefschetz Properties of Monomial Ideals with Almost Linear Resolution [Elektronisk resurs]
No full textWe study the WLP and SLP of artinian monomial ideals in S = K[x1, . . . , xn]via studying their minimal free resolutions. We study the Lefschetz properties of such idealswhere the minimal free resolution of S/I is linear for at least n − 2 steps. We give anaffirmative answer to a conjecture of Eisenbud, Huneke and Ulrich for artinian monomialideals with almost linear resolutions.</p
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