6533b7d6fe1ef96bd12665a9
RESEARCH PRODUCT
Multiprojective spaces and the arithmetically Cohen-Macaulay property
Giuseppe FavacchioJuan C. Miglioresubject
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 - Geometrialinkagedescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-05-01 |