  In this text we signal a serious gap in the proof of the main theorem of our
paper and explain which parts of the statement remain valid. In fact, the main
theorem remains valid unless possibly the variety does not admit
positive-dimensional subvarieties through a very general point and is not
bimeromorphic to a quotient of a torus. This latter case would be ruled out by
a Chern class inequality which holds in the algebraic case but is still unknown
in the K\"ahler setting.
