Generalized Chow Forms and Reduction of Semi-Stable Varieties

In this note, by using the method of S. Zhang [1], we obtain the local version of a theorem of BGS [2] which links Faltings heights of projective varieties with the Philippon heights for the corresponding generalized Chow points. By the stable reduction theorem of S. Zhang [1], we prove that Chow semistabilities and generalized Chow semistabilities are the same.