Search results for "Configuration of lines"

showing 2 items of 2 documents

Special arrangements of lines: Codimension 2 ACM varieties in P 1 × P 1 × P 1

2019

In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.

Pure mathematicsAlgebra and Number TheoryMathematics::Commutative AlgebraConfiguration of linesApplied Mathematics010102 general mathematicsarithmetically Cohen-Macaulay; Configuration of lines; multiprojective spaces0102 computer and information sciencesCodimension01 natural sciencesSettore MAT/02 - Algebraarithmetically Cohen-Macaulay010201 computation theory & mathematicsarithmetically Cohen–Macaulay Configuration of lines multiprojective spacesArithmetically Cohen-Macaulay Configuration of lines multiprojective spacesComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONSettore MAT/03 - Geometria0101 mathematicsarithmetically Cohen–Macaulaymultiprojective spacesMathematics
researchProduct

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
researchProduct