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Polarized minimal families of rational curves and higher Fano manifolds
In this paper we investigate Fano manifolds whose Chern characters
satisfy some positivity conditions. Our approach is via the study of
polarized minimal families of rational curves through a general
point . First we translate positivity properties of the Chern
characters of into properties of the pair . This allows us to
classify polarized minimal families of rational curves associated to Fano
manifolds satisfying and . As a first
application, we provide sufficient conditions for these manifolds to be covered
by subvarieties isomorphic to and . Moreover, this
classification enables us to find new examples of Fano manifolds satisfying
.Comment: 17 page
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