We construct complex projective schemes with Lyubeznik numbers of their cones depending on the choices of projective embeddings. This answers a question of G. Lyubeznik in the characteristic 0 case. It contrasts with a theorem of W. Zhang in the positive characteristic case where the Frobenius endomorphism is used. Reducibility of schemes is essential in our argument. B. Wang recently constructed examples of irreducible projective schemes (which are not normal) from our examples of reducible ones. So the question is still open in the normal singular case.

中文翻译：

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射影方案的圆锥面的吕贝兹尼克数对射影嵌入的依赖性

我们根据投影嵌入的选择，使用圆锥的Lyubeznik数构造复杂的投影方案。这回答了特征0案件中的G. Lyubeznik问题。在使用Frobenius同态的正特征情况下，这与W. Zhang定理相反。方案的可简化性在我们的论点中至关重要。B. Wang最近从我们的可约化方案实例中构造了不可约化投影方案的实例（这是不正常的）。因此，在通常的奇异情况下，这个问题仍然存在。