Fano manifolds and blow-ups of low-dimensional subvarieties

Details Fano manifolds and blow-ups of low-dimensional subvarieties Fano manifolds and blow-ups of low-dimensional subvarieties

2007-09-20

arxiv.org/abs/0709.3200v1

Mathematics

Algebraic Geometry

Scientific paper

We study Fano manifolds of pseudoindex greater than one and dimension greater
than five, which are blow-ups of smooth varieties along smooth centers of
dimension equal to the pseudoindex of the manifold. We obtain a classification
of the possible cones of curves of these manifolds, and we prove that there is
only one such manifold without a fiber type elementary contraction.

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