6533b862fe1ef96bd12c6d3e
RESEARCH PRODUCT
Tower sets and other configurations with the Cohen-Macaulay property
Alfio RagusaGiuseppe FavacchioGiuseppe Zappalàsubject
MonomialTower setBetti sequence; Cohen-Macaulay; Tower setCommutative Algebra (math.AC)Combinatoricssymbols.namesake13H10 14N20 13D40FOS: MathematicsMathematicsmonomial idealsHilbert series and Hilbert polynomialAlgebra and Number TheoryIdeal (set theory)Mathematics::Commutative AlgebraCohen–Macaulay propertyMonomial idealCodimensionBetti sequenceMathematics - Commutative AlgebraTower (mathematics)Arithmetically Cohen-MacaulayCohen-MacaulayPrimary decompositionSettore MAT/02 - AlgebraScheme (mathematics)Hilbert functionsymbolsSettore MAT/03 - GeometriaCohen–Macaulay property monomial ideals Hilbert function.description
Abstract Some well-known arithmetically Cohen–Macaulay configurations of linear varieties in P r as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z + c called tower set. We prove that the tower schemes are arithmetically Cohen–Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen–Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes (in codimension 2). Our main result consists in showing that the support of these configurations (the generalized tower set) gives a combinatorial characterization of the primary decomposition of the arithmetically Cohen–Macaulay squarefree monomial ideals.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-01-15 |