Search results for "Polynomial ring"

showing 4 items of 4 documents

Steiner systems and configurations of points

2020

AbstractThe aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner SystemS(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configur…

Linear codes; Monomial ideals; Stanley Reisner rings; Steiner systems; Symbolic powersSteiner systemsBetti numberPolynomial ring0102 computer and information sciencesAlgebraic geometrySymbolic powers01 natural sciencessymbols.namesakeMathematics - Algebraic GeometryLinear codesTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYMonomial idealsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsMathematics - CombinatoricsIdeal (ring theory)0101 mathematicsCommutative algebraAlgebraic Geometry (math.AG)Complement (set theory)MathematicsDiscrete mathematicsHilbert series and Hilbert polynomialApplied Mathematics010102 general mathematicsStanley Reisner ringsLinear codes Monomial ideals Stanley Reisner rings Steiner systems Symbolic powersComputer Science Applications51E10 13F55 13F20 14G50 94B27Settore MAT/02 - AlgebraSteiner systemSteiner systems Monomial ideals Symbolic powers Stanley Reisner rings Linear codes010201 computation theory & mathematicssymbolsCombinatorics (math.CO)Settore MAT/03 - GeometriaMathematicsofComputing_DISCRETEMATHEMATICS
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Locally tame plane polynomial automorphisms

2010

Abstract For automorphisms of a polynomial ring in two variables over a domain R , we show that local tameness implies global tameness provided that every 2-generated locally free R -module of rank 1 is free. We give examples illustrating this property.

PolynomialRank (linear algebra)Polynomial ringPolynomial automorphismsCommutative Algebra (math.AC)01 natural sciencesCombinatoricsMathematics - Algebraic GeometryFOS: MathematicsAlgebra en Topologie0101 mathematicsAlgebraic Geometry (math.AG)MathematicsAlgebra and TopologyAlgebra and Number TheoryPlane (geometry)local tameness010102 general mathematicsA domainMathematics - Commutative AlgebraAutomorphism[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]010101 applied mathematicsComputingMethodologies_DOCUMENTANDTEXTPROCESSING[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]14R10Journal of Pure and Applied Algebra
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The Herzog-Vasconcelos conjecture for affine semigroup rings

1999

Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.

Discrete mathematicsPure mathematicsRing (mathematics)Algebra and Number TheoryConjectureMathematics::Commutative AlgebraSemigroupPolynomial ringDimension (graph theory)Affine transformationMathematicsMathematicsIndraStra Global
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On the regularity and defect sequence of monomial and binomial ideals

2018

When S is a polynomial ring or more generally a standard graded algebra over a field K, with homogeneous maximal ideal m, it is known that for an ideal I of S, the regularity of powers of I becomes eventually a linear function, i.e., reg(Im) = dm + e for m ≫ 0 and some integers d, e. This motivates writing reg(Im) = dm + em for every m ⩾ 0. The sequence em, called the defect sequence of the ideal I, is the subject of much research and its nature is still widely unexplored. We know that em is eventually constant. In this article, after proving various results about the regularity of monomial ideals and their powers, we give several bounds and restrictions on em and its first differences when…

MonomialPure mathematicsIdeal (set theory)Mathematics::Commutative AlgebraBinomial (polynomial)Polynomial ring010102 general mathematicsGraded ringMonomial ideal01 natural sciencesPrimary decompositionMaximal ideal0101 mathematicsMathematicsCzechoslovak Mathematical Journal
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