The Castelnuovo-Mumford regularity of an integral variety of a vector field on projective space

Details The Castelnuovo-Mumford regularity of an integral variety of a vector field on projective space The Castelnuovo-Mumford regularity of an integral variety of a vector field on projective space

2000-11-02

arxiv.org/abs/math/0011018v1

Mathematics

Algebraic Geometry

15 pages, La-TeX

Scientific paper

The Castelnuovo-Mumford regularity r of a complex, projective variety V is an upper bound for the degrees of the hypersurfaces necessary to cut out V. In this note we give a bound for r when V is left invariant by a vector field on the ambient projective space. More precisely, assume V is arithmetically Cohen-Macaulay, for instance, a complete intersection. Assume as well that V projects to a normal-crossings hypersurface, which is the case when V is a curve with at most ordinary nodes. Then we show that r

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