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Effective local finite generation of multiplier ideal sheaves

Dan Popovici (2010)

Annales de l’institut Fourier

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

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