On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates both the description and computation via Morse theory of key topological invariants. Here we establish checkable conditions under which the behavior at infinity may be ignored, and the usual theorems of classical and stratified Morse theory may be applied. This allows for simplified arguments in the field of analytic combinatorics in several variables, and forms the basis for new methods applying to problems beyond the reach of previous techniques.

中文翻译：

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分析组合学的无穷大静止点

在复杂的代数簇上，组合应用中出现的高度函数不合适。这使通过关键拓扑不变量的莫尔斯理论的描述和计算变得复杂。在这里，我们建立了可以忽略无穷远行为的可检查条件，并且可以应用经典和分层莫尔斯理论的常用定理。这允许在多个变量的分析组合领域中简化论证，并形成应用于解决先前技术无法实现的问题的新方法的基础。