${\aleph }_0$-categorical strongly minimal compact complex manifolds

Abstract

Essential ${\aleph }_0$-categoricity; i.e., ${\aleph }_0$-categoricity in some full countable language, is shown to be a robust notion for strongly minimal compact complex manifolds. Characterisations of triviality and essential ${\aleph }_0$-categoricity are given in terms of complex-analytic automorphisms, in the simply connected case, and correspondences in general. As a consequence it is pointed out that an example of McMullen yields a strongly minimal compact Kähler manifold with trivial geometry but which is not ${\aleph }_0$-categorical, giving a counterexample to a conjecture of the second author and Tom Scanlon.

16 pages

References in corpus (1)

• Automorphisms and autoequivalences of generic analytic K3 surfaces