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Division theorems and twisted complexes

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Abstract

We prove new Skoda-type division, or ideal membership, theorems. We work in a geometric setting of line bundles over Kahler manifolds that are Stein away from an analytic subvariety. (This includes complex projective manifolds.) Our approach is to combine the twisted Bochner-Kodaira Identity, used in the Ohsawa-Takegoshi Theorem, with Skoda’s basic estimate for the division problem. Techniques developed by McNeal and the author are then used to provide many examples of new division theorems. Among other applications, we give a modification of a recent result of Siu regarding effective finite generation of certain section rings.

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Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, USA

    Dror Varolin

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  1. Dror Varolin
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Correspondence to Dror Varolin.

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Partially supported by NSF grant DMS-0400909.

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Varolin, D. Division theorems and twisted complexes. Math. Z. 259, 1–20 (2008). https://doi.org/10.1007/s00209-007-0133-4

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  • DOI: https://doi.org/10.1007/s00209-007-0133-4

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