Asymptotic syzygies of algebraic varieties

By L. Ein, R. Lazarsfeld. 2011

85 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/314e67c4e7e3363f20d0f06446aa386573e93067

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In Algebra and Number Theory

1. Uwe Nagel
2. Juan Migliore
3. Karim A. Adiprasito

In Computational Theory and Mathematics

1. Tim Roemer
2. Uwe Nagel
3. Juan Migliore
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In Geometry and Topology

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2. Juan Migliore
3. Karim A. Adiprasito

Citations in the corpus

• Secant varieties of Segre–Veronese varieties (2010, unknown): “For Veronese varieties, the asymptotic picture of the Betti tables is described in work of Ein and Lazarsfeld [EL11].”
• Equivariant Hilbert Series in non-Noetherian Polynomial Rings (2015, background): “nvariant for suitably large integers i. Analyzing properties of invariants by studying them asymptotically has become a systematic approach in commutative algebra only in the last decades (see, e.g., [2, 3, 6, 10, 11, 14]). The mentioned rationality result allows us to asymptotically determine the K”