Search results for " 13C40"

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Multiprojective spaces and the arithmetically Cohen-Macaulay property

2019

AbstractIn this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for ℙ1× ℙ1and, more recently, in (ℙ1)r. In ℙ1× ℙ1the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in ℙm× ℙn. In such an ambient space it is equivalent to the so-called (⋆)-property. Moreover, we start an investigation of the ACM property in ℙ1× ℙn. We give a new construction that highlights how different the behavior of the ACM property is in this setting.

Pure mathematicsArithmetically Cohen-Macaulay multiprojective spacesProperty (philosophy)points in multiprojective spaces arithmetically Cohen-Macaulay linkageGeneral MathematicsStar (graph theory)Space (mathematics)Commutative Algebra (math.AC)01 natural sciencesMathematics - Algebraic Geometryarithmetically Cohen-MacaulayTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY0103 physical sciencesFOS: Mathematics0101 mathematicsAlgebraic Geometry (math.AG)Mathematics010102 general mathematics14M05 13C14 13C40 13H10 13A15Mathematics - Commutative Algebrapoints in multiprojective spacesAmbient spaceSettore MAT/02 - Algebra010307 mathematical physicsSettore MAT/03 - Geometrialinkage
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A remark on hyperplane sections of rational normal scrolls

2017

We present algebraic and geometric arguments that give a complete classification of the rational normal scrolls that are hyperplane section of a given rational normal scrolls.

TheoryofComputation_MISCELLANEOUSMathematics::Commutative AlgebraInformationSystems_INFORMATIONINTERFACESANDPRESENTATION(e.g.HCI)Determinantal idealsMSC: Primary 14M12 13C40Quantitative Biology::Tissues and Organs[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Commutative AlgebraCommutative Algebra (math.AC)[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Algebraic GeometryComputingMethodologies_PATTERNRECOGNITIONMathematics::Algebraic GeometryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputingMethodologies_DOCUMENTANDTEXTPROCESSINGFOS: MathematicsRational normal scrolls[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Nonlinear Sciences::Pattern Formation and SolitonsAlgebraic Geometry (math.AG)
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