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 $ au_L(R):=-K_XcdotGamma/(L cdot Gamma)$, where $Gamma$ is a minimal curve of an extremal ray $R:=mathbb R_+[Gamma]$ on $X$ such that $L cdot R>0$.
Extremal rays of non-integral $L$-length
NOVELLI, CARLA
2013-01-01
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 $ au_L(R):=-K_XcdotGamma/(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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