Inventiones mathematicae

, Volume 190, Issue 3, pp 603–646 | Cite as

Asymptotic syzygies of algebraic varieties



We study the asymptotic behavior of the syzygies of a smooth projective variety as the positivity of the embedding line bundle grows. The main result asserts that the syzygy modules are non-zero in almost all degrees allowed by Castelnuovo–Mumford regularity. We also give an effective statement for Veronese varieties that we conjecture to be optimal.


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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity Illinois at ChicagoChicagoUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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