Aubin-Yau泛函的渐近斜率和Donaldson-Futaki不变量的计算
Asymptotic slopes of the Aubin-Yau functional and calculation of the Donaldson-Futaki invariant
摘要：
我们推导出一个明确的公式的Aubin-Yau功能沿Bergman测地线上的复杂的维2的表面上，扩展的工作Phong-Sturm黎曼曲面。这相当于一个显式计算的Donaldson-Futaki不变量的测试配置。斜率被给出为求和为有理数的有理函数的周期积分的有理线性组合。这一结果给出了一种直接检验二维射影簇是否K-稳定的方法。
英文摘要：
We derive an explicit formula for the asymptotic slope of the Aubin-Yau functional along a Bergman geodesic on a surface of complex dimension 2, extending the work of Phong-Sturm on Riemann surfaces. This is equivalent to an explicit calculation of the Donaldson-Futaki invariant of a test configuration. The slope is given as a rational linear combination of period integrals of rational functions that sum to a rational number. The result gives a way to check directly whether a two dimensional projective variety is K-stable.
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。
