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Mathematics > Algebraic Geometry

arXiv:2201.00839 (math)
[Submitted on 3 Jan 2022 (v1), last revised 8 Dec 2023 (this version, v2)]

Title:Koszul modules with vanishing resonance in algebraic geometry

Authors:Marian Aprodu, Gavril Farkas, Claudiu Raicu, Jerzy Weyman
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Abstract:We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace in the second wedge product of a vector space. Previously Koszul modules of finite length have been used to give a proof of Green's Conjecture on syzygies of generic canonical curves. We now give applications to effective stabilization of cohomology of thickenings of algebraic varieties, divisors on moduli spaces of curves, enumerative geometry of curves on K3 surfaces and to skew-symmetric degeneracy loci. We also show that the stability of sufficiently positive rank 2 vector bundles on curves is governed by resonance.
Comments: 28 pages. To appear in Selecta Math
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
Cite as: arXiv:2201.00839 [math.AG]
  (or arXiv:2201.00839v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2201.00839

Submission history

From: Gavril Farkas [view email]
[v1] Mon, 3 Jan 2022 19:03:36 UTC (30 KB)
[v2] Fri, 8 Dec 2023 14:51:58 UTC (31 KB)
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