Bergman functions and the equivalence problem of singular domains

Abstract

In this article, we use the Bergman function, which is introduced by the second author in $\href{ https://dx.doi.org/10.4310/MRL.2004.v11.n6.a8}{[\textrm{Ya}]}$, to study the equivalence problem of bounded complete Reinhardt domains in the singular variety $\widetilde{V} = \lbrace (u_1, u_2, u_3, u_4) \in \mathbb{C}^4 \vert u_1 u_4 = u_2 u_3 \rbrace$.