局部有界有理函数的几何
The Geometry of Locally Bounded Rational Functions
AI总结：
本文研究了非奇异实代数簇上局部有界有理函数的几何，在任意维度建立基本代数与几何结果并推导出 Łojasiewicz 不等式，同时在二维情形下证明了其代数与几何间的常见对应关系。
摘要：
本文研究了非奇异实代数簇上局部有界有理函数的几何。首先在任意维度上建立了这些函数的各种基本几何与代数结果，最终推导出一个版本的 Łojasiewicz 不等式。该几何理论在二维情形下得到进一步发展，证明了这些函数的代数与几何之间存在诸多常见对应关系，这些关系与复代数几何及实代数几何中其他函数类（如 regulous functions）所预期的相符。
英文摘要：
This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating with a version of Łojasiewicz's inequality. The geometry is further developed for the case of dimension 2, where it can be shown that there exist many of the usual correspondences between the algebra and geometry of these functions that one expects from complex algebraic geometry and from other classes of functions in real algebraic geometry such as regulous functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
