Extremal rays of non-integral \(L\)-length (Q2393577)

Let \(X\) be smooth complex projective variety whose canonical bundle \(K_X\) is not nef, let \(L\) be a line bundle on \(X\) and \(R\) a Mori extremal ray of \(X\) (i.e. a ray on which \(K_X\) is not nef) such that \(L \cdot R>0\). Given a rational curve \(\Gamma\) of minimal degree in \(R\) one can define the \(L\)-length of the ray as \(\tau_L=\ell(R)/L \cdot R\), where \(\ell(R)\) is the length of the ray in the usual meaning. In the paper under review the author describes the structure of the prepolarized manifold \((X,L)\) under the assumptions that \(\tau_L\) is not integral and bigger than \((\dim X)/2-2\).