Hopf surface

In complex geometry, a Hopf surface is a compact complex surface obtained as a quotient of the complex vector space by a free action of a discrete group. If this group is the integers the Hopf surface is called primary, otherwise it is called secondary. The first example was found by Heinz Hopf, with the discrete group isomorphic to the integers, with a generator acting on by multiplication by 2; this was the first example of a compact complex surface with no Kähler metric.

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