Math @ Duke

Publications [#243932] of Ezra Miller
Papers Published
 with Shin Yao Jow, , Multiplier ideals of sums via cellular resolutions,
Mathematical Research Letters, vol. 15 no. 2
(2008),
pp. 359373, ISSN 10732780 [MR2009b:14004], [math.AG/0703299]
(last updated on 2017/12/14)
Abstract: Fix nonzero ideal sheaves a 1 , . . . ., a r and b on a normal ℚGorenstein complex variety X. For any positive real numbers α and β, we construct a resolution of the multiplier ideal script T((a 1 + . . . + a r ) α b β ) by sheaves that are direct sums of multiplier ideals script T(a 1 λ1 . . . a r λr b β ) for various λ ε ℝ ≥0 r satisfying Σ i=1 r λ i = α. The resolution is cellular, in the sense that its boundary maps are encoded by the algebraic chain complex of a regular CWcomplex. The CWcomplex is naturally expressed as a triangulation Δ of the simplex of nonnegative real vectors λ ε ℝ r with Σ i=1 r λ i = α. The acyclicity of our resolution reduces to that of a cellular free resolution, supported on Δ, of a related monomial ideal. Our resolution implies the multiplier ideal sum formula generalizing Takagi's formula for two summands [Tak05] , and recovering Howald's multiplier ideal formula for monomial ideals [How01] as a special case. Our resolution also yields a new exactness proof for the Skoda complex [Laz04, Section 9.6.C] . © International Press 2008.


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