Multiplier ideals of sums via cellular resolutions

Abstract

Abstract. Fix nonzero ideal sheaves a 1 , . . . , ar and b on a normal Q-Gorenstein complex variety X. For any positive real numbers α and β, we construct a resolution of the multiplier ideal J ((a 1 + · · · + ar) α b β ) by sheaves that are direct sums of multiplier ideals J (aThe resolution is cellular, in the sense that its boundary maps are encoded by the algebraic chain complex of a regular CW-complex. The CW-complex is naturally expressed as a triangulation ∆ of the simplex of nonnegative real vectors λ ∈ R r with P r i=1 λ i = α. The acyclicity of our resolution reduces to that of a cellular free resolution, supported on ∆, of a related monomial ideal. Our resolution implies the multiplier ideal sum formula

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