The Connectedness of Space Curve Invariants

Details The Connectedness of Space Curve Invariants The Connectedness of Space Curve Invariants

1994-01-28

arxiv.org/abs/alg-geom/9401009v1

Mathematics

Algebraic Geometry

18 pages, Latex v2.09

Scientific paper

It is a result of Gruson and Peskine that the invariants of a set points in $\ptwo$ in general position are connected. Associated to a space curve there are sequences of invariants which generalize the invariants of points in $\ptwo$. The main result of this paper is to show that the invariants of reduced, irreducible, non-degenerate curves in $\pthree$ also satisfy a connectedness property. This result greatly restricts the kinds of Borel-fixed monomial ideals which can occur as generic initial ideals of such curves and thus gives us more control over their Hilbert functions.

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