When \(K+(n-4)L\) fails to be nef (Q1313593)

Let \(X\) be a smooth projective variety of dimension \(n\) and let \(L\) be an ample line bundle on \(X\). In this paper the author studies the polarized pairs \((X,L)\) for which \(K+(n-3)L\) is nef but \(K+(n-4)L\) fails to be nef. As main tools she uses Mori theory, the Kawamata-Shokurov contraction theorem and a theorem of Wisniewski on the locus of an extremal ray.