Lifting monomial ideals

J. Migliore, U. Nagel

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We show how to lift any monomial ideal J in n variables to a saturated ideal I of the same codimension in n + t variables. We show that I has the same graded Betti numbers as J and we show how to obtain the matrices for the resolution of I. The cohomology of I is described. Making general choices for our lifting, we show that I is the ideal of a reduced union of linear varieties with singularities that are "as small as possible" given the cohomological constraints. The case where J is Artinian is the nicest. In the case of curves we obtain stick figures for I, and in the case of points we obtain certain k-configurations which we can describe in a very precise way.

Original languageEnglish
Pages (from-to)5679-5701
Number of pages23
JournalCommunications in Algebra
Issue number12
StatePublished - 2000

ASJC Scopus subject areas

  • Algebra and Number Theory


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