• Corpus ID: 239768393

Asymptotic vanishing of syzygies of algebraic varieties

@inproceedings{Park2021AsymptoticVO,
  title={Asymptotic vanishing of syzygies of algebraic varieties},
  author={Jinhyung Park},
  year={2021}
}
The purpose of this paper is to prove Ein–Lazarsfeld’s conjecture on asymptotic vanishing of syzygies of algebraic varieties. This result, together with Ein–Lazarsfeld’s asymptotic nonvanishing theorem, describes the overall picture of asymptotic behaviors of the minimal free resolutions of the graded section rings of line bundles on a projective variety as the positivity of the line bundles grows. Previously, Raicu reduced the problem to the case of products of three projective spaces, and we… 

References

SHOWING 1-10 OF 30 REFERENCES
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
The gonality conjecture on syzygies of algebraic curves of large degree
We show that a small variant of the methods used by Voisin in her study of canonical curves leads to a surprisingly quick proof of the gonality conjecture of Green and the second author, asserting
Syzygies of projective varieties of large degree: Recent progress and open problems
This paper is a survey of recent work on the asymptotic behavior of the syzygies of a smooth complex projective variety as the positivity of the embedding line bundle grows. After a quick overview
A quick proof of nonvanishing for asymptotic syzygies
We give a quick new approach to proving the main cases of the nonvanishing theorems of the rst and third authors concerning the asymptotic behavior of the syzygies of a projective variety as the
On the (non-)vanishing of syzygies of Segre embeddings
We analyze the vanishing and non-vanishing behavior of the graded Betti numbers for Segre embeddings of products of projective spaces. We give lower bounds for when each of the rows of the Betti
Schur asymptotics of Veronese syzygies
We study the asymptotic behavior of Veronese syzygies as representations of the general linear group. For a fixed homological degree p of the syzygies, we describe the exact asymptotic growth for the
Projective normality and syzygies of algebraic surfaces
In this work we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic
Representation stability for syzygies of line bundles on Segre–Veronese varieties
The rational homology groups of the packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces
Asymptotics of random Betti tables
The purpose of this paper is twofold. First, we present a conjecture to the effect that the ranks of the syzygy modules of a smooth projective variety become normally distributed as the positivity of
Syzygies of abelian varieties
Let A be an ample line bundle on an abelian variety X (over an algebraically closed field). A theorem of Koizumi ([Ko], [S]), developing Mumford's ideas and results ([M]), states that if m > 3 the
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