The paper states
Theorem 1.1
In Minimal models and Mori fibre spaces for generalized log canonical Q-pairs
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Seven other possible matches are listed below the card, among them Corollary 1.2 (Ordinary log canonical pairs) in the same paper and Theorem 1.2 in Numerical semiampleness of nef adjoint classes on compact Kähler manifolds.
Let k be an algebraically closed field of characteristic zero, and let (X,B+M) be a projective generalized log canonical \Q-pair. Thus X is normal and integral, B is an effective rational boundary, and M is the trace of a nef rational Cartier divisor on a higher projective birational model, with K_X+B+M \Q-Cartier.
There are a normal integral projective variety Y and a birational map \phi\colon X\dashrightarrow Y whose inverse contracts no divisors such that, writing B_Y=\phi_*B and taking M_Y to be the trace of the same nef b-divisor, the generalized pair (Y,B_Y+M_Y) is log canonical and
for every prime divisor E over their common function field. The inequality is strict for every divisor on X contracted by \phi. More precisely, the following alternatives are determined by D=K_X+B+M:
- 1.
if D is pseudo-effective, then K_Y+B_Y+M_Y is nef;
- 2.
if D is not pseudo-effective, there is a projective contraction h\colon Y\to T to a normal projective variety with connected fibres such that
\dim T<\dim Y,\qquad \rho(Y/T)=1, \qquad -(K_Y+B_Y+M_Y)\text{ is ample over }T.