Lifting Monomial Ideals

Details Lifting Monomial Ideals Lifting Monomial Ideals

1999-07-07

arxiv.org/abs/math/9907045v1

Mathematics

Commutative Algebra

LaTeX, 26 pages

Scientific paper

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.

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