  We establish precise nonvanishing results for asymptotic syzygies of smooth
projective varieties. This refines Ein-Lazarsfeld's asymptotic nonvanishing
theorem. Combining with the author's previous asymptotic vanishing result, we
completely determine the asymptotic shapes of the minimal free resolutions of
the graded section modules of a line bundle on a smooth projective variety as
the positivity of the embedding line bundle grows.
