The generic initial ideals of a given ideal are rather recent invariants. Not much is known about these objects, and it turns out to be very difficult to compute them. The main purpose of this paper is to study the behaviour of generic initial ideals with respect to the operation of taking distractions. Theorem 4.3 is our main result. It states that the DegRevLex-generic initial ideal of the distraction of a strongly stable ideal is the ideal itself. In proving this fact we develop some new results related to distractions, stable and strongly stable ideals. We draw some geometric conclusions for ideals of points.
Generic initial ideals and distractions
BIGATTI, ANNA MARIA;CONCA, ALDO;ROBBIANO, LORENZO
2005-01-01
Abstract
The generic initial ideals of a given ideal are rather recent invariants. Not much is known about these objects, and it turns out to be very difficult to compute them. The main purpose of this paper is to study the behaviour of generic initial ideals with respect to the operation of taking distractions. Theorem 4.3 is our main result. It states that the DegRevLex-generic initial ideal of the distraction of a strongly stable ideal is the ideal itself. In proving this fact we develop some new results related to distractions, stable and strongly stable ideals. We draw some geometric conclusions for ideals of points.
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