Abstract
We exhibit an example of a line bundle M on a smooth complex projective variety Y s.t. M satisfies Property N 10 , the 10-module of a minimal resolution of the ideal of the embedding of Y by M is nonzero and M 2 does not satisfy Property N 10 . Thus this is a completely convincing example showing that surprisingly it is not true that if a line bundle M satisfies Property N p then any power of M satisfies Property N p . We recall that in [Ru] we proved the following statement: if M is a line bundle on a smooth complex projective variety and M satisfies Property N p then M s satisfies Property N p if s≥p.
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