A smooth holomorphically convex disc in 𝐶² that is not locally polynomially convex

Forstnerič, Franc

doi:10.1090/S0002-9939-1992-1101982-0

A smooth holomorphically convex disc in $\textbf {C}^ 2$ that is not locally polynomially convex
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Proc. Amer. Math. Soc. 116 (1992), 411-415 Request permission

Abstract:

We construct a smooth embedded disc in ${{\mathbf {C}}^2}$ that is totally real except at one point $p$, is holomorphically convex, but fails to be locally polynomially or even rationally convex at $p$.

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