Search results for "Macau"

showing 3 items of 13 documents

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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Ἀνὰ μέσον ἡδονῆςτε καὶ λύπης: Avidità umana e filantropia alla prova dell’oro in Diodoro

2021

In the Third book of his Bibliotheca, Diodorus Siculus includes an account of the Egyptian gold mines and describes the terrible living conditions of the slaves who are exploited to extract the metal. In this regard, Diodorus’ source is the historian Agatharchides of Cnidus, whose account is handed down by the Byzantine writer Photius. The comparison between the two texts allows scholars to highlight the different historical perspective of Diodorus, which privileges a worldview dominated by philanthropy and compassion for the most peripheral humanity. Further confirmation arises from the description of the Iberian mines (V 35-38), which Diodorus derives from the historian and philosopher Po…

Settore L-ANT/02 - Storia GrecaDiodorus Macaulay philanthropy compassion human condition greed koinè historia didactic function
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The ACM property for unions of lines in P1×P2

2021

This paper examines the Arithmetically Cohen-Macaulay (ACM) property for certain codimension 2 varieties in P1×P2 called sets of lines in P1×P2 (not necessarily reduced). We discuss some obstacles to finding a general characterization. We then consider certain classes of such curves, and we address two questions. First, when are they themselves ACM? Second, in a non-ACM reduced configuration, is it possible to replace one component of a primary (prime) decomposition by a suitable power (i.e. to “fatten” one line) to make the resulting scheme ACM? Finally, for our classes of such curves, we characterize the locally Cohen-Macaulay property in combinatorial terms by introducing the definition …

Varieties in multiprojective spacesConfiguration of linesArithmetically Cohen-Macaulay; Configuration of lines; Varieties in multiprojective spacesArithmetically Cohen-Macaulay Configuration of lines Varieties in multiprojective spacesArithmetically Cohen-Macaulay
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