On log canonical divisors that are log quasi-numerically positive

الأصل · EN

Let (X, Δ) be a four-dimensional log variety that is projective over the field of complex numbers. Assume that (X, Δ) is not Kawamata log terminal (klt) but divisorial log terminal (dlt). First we introduce the notion of "log quasi-numerically positive", by relaxing that of "numerically positive". Next we prove that, if the log canonical divisor Kₓ + Δ is log quasi-numerically positive on (X, Δ) then it is semi-ample.