Koszul modules with vanishing resonance in algebraic geometry

• Marian Aprodu ^[1] ; Gavril Farkas ^[3] ; Claudiu Raicu ^[4] ; Jerzy Weyman ^[2]
  1. [1] University of Bucharest

     University of Bucharest

     Sector 3, Rumanía

     
  2. [2] Institute of Mathematics

     Institute of Mathematics

     Warszawa, Polonia

     
  3. [3] Institut für Mathematik, Humboldt-Universität zu Berlin,Germany
  4. [4] Simion Stoilow Institute of Mathematics, Romania

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 2, 2024, págs. 1-33
• Idioma: inglés
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• Resumen

  • We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace K ⊆ 2 V, where V is 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 instability of sufficiently positive rank 2 vector bundles on curves is governed by resonance and give a splitting criterion.