Abstract
Let $X$ be a smooth complex projective variety and let $L$ be a line bundle on it. We describe the structure of the pre-polarized manifold $(X,L)$ for non integral values of the invariant $\tau_{L}(R) := -K_{X} \cdot \Gamma/(L \cdot \Gamma)$, where $\Gamma$ is a minimal curve of an extremal ray $R := \mathbb{R}_{+}[\Gamma]$ on $X$ such that $L \cdot R > 0$.
Citation
Carla Novelli. "Extremal rays of non-integral $L$-length." Osaka J. Math. 50 (2) 347 - 362, June 2013.
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