Extremal rays of non-integral L-length

2011/08/26 by Carla Novelli, Novelli, Carla
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1108.5276

13 pages

arxiv created 2011/08/26 · arxiv updated 2011/08/29

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 τ_L(R):=-K_X⋅Γ/(L ⋅ Γ), where Γ is a minimal curve of an extremal ray R:=\mathbb R₊[Γ] on X such that L ⋅ R>0.

Related

• Special rays in the Mori cone of a projective variety
• Cohomological invariants of complex manifolds coming from extremal rays
• Intersection numbers of extremal rays on holomorphic symplectic varieties
• Fano manifolds with long extremal rays
• Extremal effective curves and non-semiample line bundles on \rmM_g,n