Big line bundles on compact complex spaces satisfy a Steenbrink-type cohomology vanishing theorem after passing to a log resolution and twisting by multiplier ideal sheaves.
Demailly, Singular Hermitian metrics on positive line bundles, Proc
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Steenbrink vanishing theorem for big line bundles
Big line bundles on compact complex spaces satisfy a Steenbrink-type cohomology vanishing theorem after passing to a log resolution and twisting by multiplier ideal sheaves.