## Abstract

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 language | English |
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Pages (from-to) | 5679-5701 |

Number of pages | 23 |

Journal | Communications in Algebra |

Volume | 28 |

Issue number | 12 |

DOIs | |

State | Published - 2000 |

## ASJC Scopus subject areas

- Algebra and Number Theory