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Let be a psh function on a bounded pseudoconvex open set , and let be the associated multiplier ideal sheaves, . Motivated by global geometric issues, we establish an effective version of the coherence property of as . Namely, given any , we estimate the asymptotic growth rate in of the number of generators of over , as well as the growth of the coefficients of sections in with respect to finitely many generators globally defined on . Our approach relies on proving asymptotic integral...
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