Search results for "Hilbert Series"

showing 4 items of 14 documents

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.
researchProduct

GRADED IDENTITIES FOR THE ALGEBRA OF n×n UPPER TRIANGULAR MATRICES OVER AN INFINITE FIELD

2003

We consider the algebra Un(K) of n×n upper triangular matrices over an infinite field K equipped with its usual ℤn-grading. We describe a basis of the ideal of the graded polynomial identities for this algebra.

PolynomialHilbert series and Hilbert polynomialMathematics::Commutative AlgebraGeneral MathematicsGraded ringTriangular matrixBasis (universal algebra)Graded Lie algebraFiltered algebraAlgebrasymbols.namesakeDifferential graded algebrasymbolsMathematicsInternational Journal of Algebra and Computation
researchProduct

Cocharacters of group graded algebras and multiplicities bounded by one

2017

Let G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the (Formula presented.)-ideals (Formula presented.) of graded identities of A such that the multiplicities (Formula presented.) in the graded cocharacter of A are bounded by one. We do so by exhibiting a set of identities of the (Formula presented.)-ideal. As a consequence we characterize the varieties of G-graded algebras whose lattice of subvarieties is distributive.

Pure mathematics010103 numerical & computational mathematics01 natural sciencesGraded Lie algebraFiltered algebrasymbols.namesakeDifferential graded algebra0101 mathematicsAlgebra over a fieldMathematicsDiscrete mathematicsHilbert series and Hilbert polynomialFinite groupAlgebra and Number TheoryMathematics::Commutative AlgebraMathematics::Rings and Algebras010102 general mathematicsGraded ringPolynomial identitycocharactergraded polynomialSettore MAT/02 - AlgebraBounded functiongraded algebrasymbolsANÉIS E ÁLGEBRAS ASSOCIATIVOS
researchProduct

Expecting the unexpected: Quantifying the persistence of unexpected hypersurfaces

2021

If $X \subset \mathbb P^n$ is a reduced subscheme, we say that $X$ admits an unexpected hypersurface of degree $t$ for multiplicity $m$ if the imposition of having multiplicity $m$ at a general point $P$ fails to impose the expected number of conditions on the linear system of hypersurfaces of degree $t$ containing $X$. Conditions which either guarantee the occurrence of unexpected hypersurfaces, or which ensure that they cannot occur, are not well understand. We introduce new methods for studying unexpectedness, such as the use of generic initial ideals and partial elimination ideals to clarify when it can and when it cannot occur. We also exhibit algebraic and geometric properties of $X$ …

Pure mathematicsGeneral MathematicsComplete intersectionVector bundleAlgebraic geometrysymbols.namesakeMathematics - Algebraic GeometryAV-sequence; Complete intersection; Generic initial ideal; Hilbert function; Partial elimination ideal; Unexpected hypersurfaceUnexpected hypersurfaceFOS: MathematicsAlgebraic numberAV-sequenceAlgebraic Geometry (math.AG)Complete intersectionGeneric initial idealMathematicsHilbert series and Hilbert polynomialSequencePartial elimination idealSettore MAT/02 - AlgebraHypersurfaceHyperplanePrimary: 14C20 13D40 14Q10 14M10 Secondary: 14M05 14M07 13E10Hilbert functionsymbolsSettore MAT/03 - GeometriaAV-sequence Complete intersection Generic initial ideal Hilbert function Partial elimination ideal Unexpected hypersurface
researchProduct