Extremal rays of non-integral $L$-length

Details Extremal rays of non-integral $L$-length Extremal rays of non-integral $L$-length

2011-08-26

arxiv.org/abs/1108.5276v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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 $L \cdot R>0$.

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