Fano manifolds with long extremal rays

2005/04/13 by Marco Andreatta, Andreatta, Marco, Gianluca Occhetta +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14E30 #msc:14J45

paper · pdf · doi:10.48550/arxiv.math/0504265

arxiv created 2005/04/13 · arxiv updated 2009/12/01

Abstract

Let X be a Fano manifold of pseudoindex i_X whose Picard number is at least two and let R be an extremal ray of X with exceptional locus Exc(R). We prove an inequality which bounds the length of R in terms of i_X and of the dimension of Exc(R) and we investigate the border cases. In particular we classify Fano manifolds X of pseudoindex i_X obtained blowing up a smooth variety Y along a smooth subvariety T such that dim T < i_X.

Related

• Fano manifolds having (n-1,0)-type extremal rays with large Picard number
• Smooth Fano varieties with pseudoindex equal to half of their dimension
• On the minimal length of extremal rays for Fano 4-folds
• ACC for minimal lengths of extremal rays for surfaces
• Fano manifolds obtained by blowing up along curves with maximal Picard number