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Fano manifolds with long extremal rays

Research paper by Marco Andreatta, Gianluca Occhetta

Indexed on: 13 Apr '05Published on: 13 Apr '05Published in: Mathematics - Algebraic Geometry



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.