Universal Secant Bundles and Syzygies of Canonical Curves
arXiv:2003.05849 · doi:10.1007/s00222-020-01001-5
Abstract
We introduce a relativization of the secant sheaves used by Ein, Green and Lazarsfeld and apply this construction to the study of syzygies of canonical curves. As a first application, we give a simpler proof of Voisin's Theorem for general canonical curves. This completely determines the terms of the minimal free resolution of the coordinate ring of such curves. Secondly, in the case of curves of even genus, we enhance Voisin's Theorem by providing a structure theorem for the last syzygy space, resolving the Geometric Syzygy Conjecture in even genus.
arXiv commentFinal version, to appear in Inventiones Math. The statements concerning positive characteristic have been removed and will be published separately. This submission supersedes arXiv:1910.06200 and arXiv:1907.07553
References in corpus (6)
- Asymptotic syzygies of algebraic varieties
- Green's Conjecture for curves on arbitrary K3 surfaces
- Koszul modules and Green's conjecture
- Stability of rank-3 Lazarsfeld-Mukai bundles on K3 surfaces
- Generic Syzygy Schemes
- Geometric Syzygies of Mukai Varieties and General Canonical Curves with Genus at most 8