Complete classification of Fano manifolds

Establish a complete classification of Fano manifolds in arbitrary dimension, extending the classifications currently known only through dimension three and the partial results available in dimension four.

Background

The paper places its classification of prime Fano fourfolds within the broader program of classifying Fano manifolds. It notes that only finitely many deformation families occur in each dimension, but that a complete classification is known only up to dimension three. Dimension four has only partial classifications and databases of known families. The work addresses one specific part of this larger problem by classifying prime Fano fourfolds of Picard rank one and index one that arise as zero loci of completely reducible homogeneous vector bundles in generalized Grassmannians of non-A_n Dynkin type; it therefore does not resolve the general classification problem.