Special arrangements of lines: codimension two ACM varieties in \mathbb P¹×\mathbb P¹×\mathbb P¹

2017/07/21 by Favacchio, Giuseppe, Guardo, Elena, Picone, Beatrice
#13A15 #13C40 #13F20 #14C20 #14M05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.06863

Abstract

In this paper we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimensional two arithmetically Cohen-Macaulay (ACM) varieties in \mathbb P¹×\mathbb P¹×\mathbb P¹, called varieties of lines. We also describe their ACM property from combinatorial algebra point of view.

Related

• The ACM property for unions of lines in \mathbb P¹ × \mathbb P²
• On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces
• Multiprojective spaces and the arithmetically Cohen-Macaulay property
• ACM sets of points in multiprojective space
• Combinatorics of line arrangements and characteristic varieties