Principal jets of monomial ideals

The principal component of the jet scheme is the closure of the set of jets supported over the smooth points of the base scheme. It represents a large portion of the jet scheme and it can be relatively well behaved, as evidenced by a few case studies in the literature. We give a complete description of principal jets of monomial ideals, including their generators and irreducible decomposition. We also show how the Hilbert series and Betti numbers of the principal jets of a monomial ideal relate to the same invariants of the original ideal.

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