论文标题
线性方程式的半格式解决方案，具有连续的半缘系数
Semialgebraic Solutions of Linear Equations with Continuous Semialgebraic Coefficients
论文作者
论文摘要
从Charles Fefferman和JanosKollàr的结果开始，在线性方程的连续解决方案[1]中，我们采用了一种基于Fefferman Glaeser改进技术的新方法，比使用代数beemetry的技术证明了Kollàr证明的方法比Kollàr证明的更一般的结果。考虑一个线性方程系统具有半分布（不仅像[1]中）在r^n上的系数的系统，我们在r^n上存在连续和半ge的解决方案，我们获得了必要和足够的条件。这与Fefferman和Luli在平面上的半隔板部分中获得的不同[3]，因为它们陈述了平面r^2上规律性c^m的结果。更深入地，我们证明，当且仅当存在连续解决方案时，即与系统相关的Glaeser稳定束时，RN上存在连续的半gebraic解决方案。
Starting from the results of Charles Fefferman and Janos Kollàr in Continuous Solutions of Linear Equations [1], we adopt a new approach based on Fefferman's techniques of Glaeser refinement to show a more general result than the one proved by Kollàr by using techniques from algebraic geometry. Considering a system of linear equations with semialgebraic (not only polynomial as in [1]) coefficients on R^n, we get a necessary and sufficient condition for the existence of a continuous and semialgebraic solution on R^n. This is different from what Fefferman and Luli obtained in Semialgebraic Sections Over the Plane [3] since they stated their result for solutions of regularity C^m on the plane R^2. More in depth, we prove that a continuous and semialgebraic solution on Rn exists if and only if there is a continuous solution i.e., if the Glaeser-stable bundle associated to the system has no empty fiber.
