In [8], we define and partially classify fake real planes, that is, minimal
complex surfaces with conjugation whose real locus is diffeomorphic to the
euclidean real plane
. Classification results are given up to
biregular isomorphisms and up to birational diffeomorphisms. In this note, we
describe in an elementary way numerous examples of fake real planes and we
exhibit examples
... [Show full abstract] of such planes of every Kodaira dimension which are birationally diffeomorphic to .