Classification conjecture for generalized polarized Fano manifolds with l(R_1)=n
Classification conjecture for generalized polarized Fano manifolds with l(R_1)=n
Let be a Fano manifold of Picard number one and let be an ample vector bundle of rank on . Let , the extremal ray , and a minimal rational curve be as in the common setup, and set . If the length of is , then the classification conjecture. is one of the following:
This conjecture predicts a complete classification of the generalized polarized manifolds satisfying the extremal-length condition . The preceding argument establishes the listed possibilities in the cases treated there, while the full classification is posed as an open conjecture.
Sources & referencesView supporting material
Primary source
Masahiro Ohno, “Classification of generalized polarized manifolds by their nef values”, arXiv:math/0503119 (2005).
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