6533b82dfe1ef96bd12910d6
RESEARCH PRODUCT
The ACM property for unions of lines in P1×P2
G. FavacchioJ. Miglioresubject
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-Macaulaydescription
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 of a fully v-connected configuration. We apply some of our results to give analogous ACM results for sets of lines in P3.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-01-01 |