Positivity of divisors on blown-up projective spaces, II

We construct log resolutions of pairs on the blow-up of the projective space in an arbitrary number of general points and we discuss the semi-ampleness of the strict transforms. As an application we give an explicit proof that the abundance conjecture holds for an infinite family of such pairs. For n + 2 points, these strict transforms are F-nef divisors on the moduli space M0,n+3 in a Kapranov’s model: we show that all of them are nef.