S_n-Equivariant Sheaves and Kozsul Cohomology

2014/07/16 by David Yang, David H Yang, Yang, David H
Mathematics · #14F05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14F05

paper · pdf · doi:10.48550/arxiv.1407.4183

7 pages

openalex publication_date 2014/07/16 · arxiv created 2014/07/28 · arxiv updated 2014/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new interpretation of Kozsul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin's Hilbert scheme interpretation in dimensions 1 and 2, but is different in higher dimensions. As an application, we prove that the dimension K_p,q(B,L) is a polynomial in d for L=dA+P with A ample and d large enough.

Citations

• Asymptotic syzygies of algebraic varieties
• green's canonical syzygy conjecture for generic curves of odd genus
• The gonality conjecture on syzygies of algebraic curves of large degree

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