On Fano varieties whose effective divisors are numerically eventually free

In this paper we classify mildly singular Fano varieties with maximal Picard number whose effective divisors are numerically eventually free. In addition, we prove that if a Del Pezzo surface of degree $r$ admits a finite morphism of degree $\gt 1$ onto a Del Pezzo surface of degree $s$, then either $r = s \geqslant 6$, or $r \lt s$ and $s \geqslant 8$.

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Accepted 10 December 2015

Published 8 July 2016