Lifting monomial ideals |
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Authors: | J Migliore U Nagel |
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Institution: | 1. Department of mathematics , University of notre dame , Room 370 ccmb, Notre dame, 46556, U S A E-mail: juan. c. migliore. lqnd. edu;2. Fachbereich mathematik und informatik , Universit?t-gesamthochschule paderborn , Paderborn, d-33095, Germany E-mail: uwenQuni-paderborn.de |
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Abstract: | We show how to lift any monomial ideal J in n variables to a saturated ideal J 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 cohornology of l is described. Making general choices for our lifting, we show that l 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 l, and in the case of points we obtain certain k-configurations which we can describe in a very precise way. |
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