The Multiplier Ideals of a Sum of Ideals

Details The Multiplier Ideals of a Sum of Ideals The Multiplier Ideals of a Sum of Ideals

2001-02-27

arxiv.org/abs/math/0102217v2

Trans. Amer. Math. Soc. 354 (2002), no. 1, 205-217

Mathematics

Algebraic Geometry

16 pages; LaTeX. Notational and expository changes, a mistake in the statement of Proposition 2.1 is corrected; to appear in T

Scientific paper

Let X be a smooth variety and J, K two ideal sheaves on X. We prove the following formula relating the multiplier ideals of J, K and J+K: I(X, c(J+K))\subset \sum_{a+b=c} I(X, aJ)\cdot I(X,bK). An analogous formula holds for the asymptotic multiplier ideals of two graded systems of ideals. As a consequence, we show how to approximate at any given point arbitrary multiplier ideals by multiplier ideals of zero dimensional ideals. We apply this to study the invariance of multiplier ideals under different embeddings.

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