0000000000283088

AUTHOR

Alfio Ragusa

showing 2 related works from this author

Linear quotients of Artinian Weak Lefschetz algebras

2013

Abstract We study the Hilbert function and the graded Betti numbers for “generic” linear quotients of Artinian standard graded algebras, especially in the case of Weak Lefschetz algebras. Moreover, we investigate a particular property of Weak Lefschetz algebras, the Betti Weak Lefschetz Property, which makes possible to completely determine the graded Betti numbers of a generic linear quotient of such algebras.

Discrete mathematicsPure mathematicsHilbert series and Hilbert polynomialAlgebra and Number TheoryProperty (philosophy)Mathematics::Commutative AlgebraBetti numberBetti Weak Lefschetz PropertyMathematics::Rings and AlgebrasArtinian algebraLinear quotientWeak Lefschetz Propertysymbols.namesakeQuotientWeak Lefschetz; Artinian algebra; QuotientsymbolsWeak Lefschetz Property Artinian algebra Linear quotientLefschetz fixed-point theoremWeak LefschetzMathematics::Symplectic GeometryQuotientMathematics
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Tower sets and other configurations with the Cohen-Macaulay property

2014

Abstract Some well-known arithmetically Cohen–Macaulay configurations of linear varieties in P r as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z + c called tower set. We prove that the tower schemes are arithmetically Cohen–Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen–Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes …

MonomialTower setBetti sequence; Cohen-Macaulay; Tower setCommutative Algebra (math.AC)Combinatoricssymbols.namesake13H10 14N20 13D40FOS: MathematicsMathematicsmonomial idealsHilbert series and Hilbert polynomialAlgebra and Number TheoryIdeal (set theory)Mathematics::Commutative AlgebraCohen–Macaulay propertyMonomial idealCodimensionBetti sequenceMathematics - Commutative AlgebraTower (mathematics)Arithmetically Cohen-MacaulayCohen-MacaulayPrimary decompositionSettore MAT/02 - AlgebraScheme (mathematics)Hilbert functionsymbolsSettore MAT/03 - GeometriaCohen–Macaulay property monomial ideals Hilbert function.
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