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.
References
Primary source
Masahiro Ohno, “Classification of generalized polarized manifolds by their nef values”, arXiv:math/0503119 (2005).
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