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Multiplier ideal
Algebraic geometry
In algebraic geometry, the multiplier ideal of an effective
Q -divisor measures singularities coming from the fractional parts of D. Multiplier ideals are often applied in tandem with vanishing theorems such as the Kodaira vanishing theorem and the Kawamata?Viehweg vanishing theorem.
Let X be a smooth complex variety and D an effective
Q -divisor on it.
Let μ :X'→ X be a log resolution of D (e.g., Hironaka's resolution).
下記FUJINOより抜粋
P6 5. Resolution Lemma We think that one of the most useful log terminal singularities is divisorial log terminal (dlt, for short), which was introduced by Shokurov (see [FA, (2.13.3)]). We defined it in Definition 4.1 above. By Szab´o’s work [Sz], the notion of dlt coincides with that of weakly Kawamata log terminal (wklt, for short).
P7 By combining Theorem 5.1 with the usual desingularization arguments, we can recover the original Resolution Lemma without any difficulties. This means that, first, we use Hironaka’s desingularization theorem suitably, next, we apply Theorem 5.1 below, then we can recover Szab´o’s results.
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