The generalized Mukai conjecture asserts that a positive-dimensional smooth connected complex Fano manifold of dimension Picard number pseudoindex
with equality precisely when
It strengthens the index formulation by using the smallest anticanonical rational-curve
degree instead of divisibility in the Picard group .
When
See also Fano Index ,
Fano Manifold ,
Fano Pseudoindex ,
Picard
Number ,
Projective Space
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References Bonavero, L.; Casagrande, C.; Debarre, O.; and Druel, S. "Sur une conjecture de Mukai." Comment. Math. Helv. 78 , 601-626,
2003. https://doi.org/10.1007/S00014-003-0765-X .
Cite this as:
Weisstein, Eric W. "Generalized Mukai Conjecture."
From MathWorld https://mathworld.wolfram.com/GeneralizedMukaiConjecture.html
Subject classifications
,
Picard number 
, and pseudoindex 
satisfies
,
the inequality is strict since 
.
