The study of p-essentially normal Hilbert modules originates from Arveson's seminal works in which it is applied to investigate the dilation theory and the geometric invariant theory of the commuting operator tuple. Recently, the p-essential normality of Hilbert modules has continuously attracted more attention. In this talk, I shall talk about the biholomorphic invariance of p-essential normality of Hilbert modules and give some intrinsic characterizations of the p-essential normality.