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We revisit a bound on symbolic powers found by Ein-Lazarsfeld-Smith andsubsequently improved by Takagi-Yoshida. We show that the original argument ofEin-Lazarsfeld-Smith actually gives the same improvement. On the other hand, weshow by examples that any further improvement based on the same techniqueappears unlikely. This is primarily an exposition; only some examples andremarks might be new.

Bounding symbolic powers via asymptotic multiplier ideals