An Assympotic Vanishing Theorem for Generic Unions of Multiple Points

Details An Assympotic Vanishing Theorem for Generic Unions of Multiple Points An Assympotic Vanishing Theorem for Generic Unions of Multiple Points

1997-03-28

arxiv.org/abs/alg-geom/9703037v3

Mathematics

Algebraic Geometry

26 pages, Latex 2e, using diagrams.tex. Revised edition

Scientific paper

In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the following : given an ample line bundle O(1) on a projective variety X and a fixed upper bound M on the multiplicities, there exists a lower bound D such that any generic union of multiple points of multiplicity at most M imposes independent conditions on the sections of O(d) for d>D. Here a multiple point is the closed subscheme defined by a power m of the ideal of a smooth point in X and m is its multiplicity.

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