We define a variant of intersection space theory that applies to many compact complex and real analytic spaces [Formula: see text], including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to apply to a particular subclass of spaces with smooth singular sets. We verify existence of these so-called algebraic intersection spaces and show that they are the (reduced) chain complexes of known topological intersection spaces in the case that both exist. We next analyze “local duality obstructions,” which we can choose to vanish, and verify that algebraic intersection spaces satisfy duality in the absence of these obstructions. We conclude by defining an untwisted algebraic intersection space pairing, whose signature is equal to the Novikov signature of the complement in [Formula: see text] of a tubular neighborhood of the singular set.

中文翻译：

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代数交叉空间

我们定义了一种交集空间理论的变体，它适用于许多紧复实分析空间[公式：见正文]，包括所有复射影变体；这是对迄今为止仅被证明适用于具有光滑奇异集的特定空间子类的理论的重要扩展。我们验证了这些所谓的代数交叉空间的存在，并表明它们是已知拓扑交叉空间的（约简）链复形，在两者都存在的情况下。我们接下来分析“局部对偶障碍”，我们可以选择消失，并验证代数交叉空间在没有这些障碍的情况下满足对偶。我们通过定义一个非扭曲代数交集空间对来结束，其签名等于 [公式：