The Fujita freeness conjecture asserts that on a smooth projective variety 
of dimension 
, the adjoint line bundle 
is generated by global sections for every ample line bundle 
.
Additive notation denotes tensor powers and products of line
bundles. Global generation means that at every point some global section is nonzero.
It does not require 
itself to have a section.
For 
and 
,
this adjoint is trivial, whereas 
has no nonzero sections, showing sharpness of the exponent.
