We classify all minimal models X of dimension n, Kodaira dimension and with vanishing Chern number . This solves a problem of Kollár. Completing previous work of Kollár and Grassi, we also show that there is a universal constant such that any minimal threefold satisfies either or . This settles completely a conjecture of Kollár.
Funding statement: Both authors are supported by the DFG grant “Topologische Eigenschaften von Algebraischen Varietäten” (project no. 416054549). The first author is also supported by grant G097819N of Nero Budur from the Research Foundation Flanders.
The second author thanks I. Cheltsov, S. Filipazzi, Th. Peternell and C. Shramov for useful discussions. We thank the referees for their careful reading and for a question that lead us to discover the uniqueness statement in item d of Corollary 1.2.
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