Search results for "Symbolic powers"

showing 3 items of 3 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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The minimal free resolution of fat almost complete intersections in ℙ1 x ℙ1

2017

AbstractA current research theme is to compare symbolic powers of an ideal I with the regular powers of I. In this paper, we focus on the case where I = IX is an ideal deûning an almost complete intersection (ACI) set of points X in ℙ1 × ℙ1. In particular, we describe a minimal free bigraded resolution of a non-arithmetically Cohen-Macaulay (also non-homogeneous) set 𝒵 of fat points whose support is an ACI, generalizing an earlier result of Cooper et al. for homogeneous sets of triple points. We call 𝒵 a fat ACI.We also show that its symbolic and ordinary powers are equal, i.e, .

Current (mathematics)Ideal (set theory)General MathematicsPoints in ℙ1× ℙ1010102 general mathematicsComplete intersectionArithmetically Cohen-Macaulay; Points in ℙ1× ℙ1; Resolution; Symbolic powersSymbolic powers01 natural sciencesArithmetically Cohen-MacaulayCombinatoricsSet (abstract data type)Settore MAT/02 - AlgebraHomogeneous0103 physical sciencesArithmetically Cohen-Macaulay Points in ℙ1xℙ1 Resolution Symbolic powersSettore MAT/03 - Geometria010307 mathematical physics0101 mathematicsResolutionFocus (optics)Resolution (algebra)Mathematics
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Steiner configurations ideals: Containment and colouring

2021

Given a homogeneous ideal I&sube

HypergraphSteiner systemsCurrent (mathematics)General MathematicsIdeals of points Monomial ideals Steiner systems Symbolic powers of ideals Waldschmidt constantideals of points0102 computer and information sciencesCommutative Algebra (math.AC)01 natural sciencesCombinatoricsMathematics - Algebraic GeometryMonomial idealsFOS: MathematicsComputer Science (miscellaneous)Mathematics - Combinatorics13F55 13F20 14G50 51E10 94B270101 mathematicsAlgebraic Geometry (math.AG)Engineering (miscellaneous)MathematicsSymbolic powers of idealsmonomial idealsContainment (computer programming)ConjectureIdeal (set theory)Mathematics::Commutative Algebralcsh:Mathematics010102 general mathematicslcsh:QA1-939Mathematics - Commutative AlgebraIdeals of pointsWaldschmidt constantComplement (complexity)Settore MAT/02 - AlgebraSteiner systemCover (topology)010201 computation theory & mathematicssymbolic powers of idealsIdeals of points; Monomial ideals; Steiner systems; Symbolic powers of ideals; Waldschmidt constantCombinatorics (math.CO)Settore MAT/03 - Geometriamonomial ideals ideals of points symbolic powers of ideals Waldschmidt constant Steiner systems
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