Asymptotic syzygies of algebraic varieties |
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| Authors: | Lawrence Ein Robert Lazarsfeld |
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| Affiliation: | 1. Department of Mathematics, University Illinois at Chicago, 851 South Morgan St., Chicago, IL, 60607, USA
2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA
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| Abstract: | 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?CMumford regularity. We also give an effective statement for Veronese varieties that we conjecture to be optimal. |
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