关于奇异簇的横截性：张开因子
Towards transversality of singular varieties: splayed divisors
摘要：
研究了复流形中横截光滑超曲面的一种自然推广：其分支横截但自身可能奇异的超曲面。这样的超曲面称为张开因子。一个张开因子的特征在于它的雅可比理想的一个性质。这就产生了一个有效的展性测试。一个张开因子的两个进一步的特征显示，一个反映了它的组件的交集的几何形状，另一个使用K。齐藤的对数导数。作为应用，我们证明了光滑超曲面的并有正规交叉当且仅当它是自由因子且有根雅可比理想。进一步证明了张开因子的Hilbert-Samuel多项式满足一定的可加性。
英文摘要：
We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces, whose components intersect in a transversal way but may be themselves singular. Such hypersurfaces will be called splayed divisors. A splayed divisor is characterized by a property of its Jacobian ideal. This yields an effective test for splayedness. Two further characterizations of a splayed divisor are shown, one reflecting the geometry of the intersection of its components, the other one using K. Saito's logarithmic derivations. As an application we prove that a union of smooth hypersurfaces has normal crossings if and only if it is a free divisor and has a radical Jacobian ideal. Further it is shown that the Hilbert-Samuel polynomials of splayed divisors satisfy a certain additivity property.
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