Bi-graded Koszul modules, K3 carpets, and Green's conjecture

DOI10.1112/S0010437X21007703zbMath1486.14050arXiv1909.09122OpenAlexW4207085647WikidataQ113788510 ScholiaQ113788510MaRDI QIDQ5037281

Claudiu Raicu, Steven V. Sam

Publication date: 28 February 2022

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.09122

zbMATH Keywords

syzygiesKoszul modulesGreen's conjecture\(K3\) carpetscanonical ribbon conjecture

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Special algebraic curves and curves of low genus (14H45) Syzygies, resolutions, complexes and commutative rings (13D02) Divisors, linear systems, invertible sheaves (14C20) Special divisors on curves (gonality, Brill-Noether theory) (14H51) Curves in algebraic geometry (14H99)

Related Items (3)

Hermite Reciprocity and Schwarzenberger Bundles ⋮ Koszul modules of Kac-Moody Lie algebras ⋮ MFO-RIMS tandem workshop: Symmetries on polynomial ideals and varieties. Abstracts from the MFO-RIMS tandem workshop held September 5--11, 2021 (hybrid meeting)

Uses Software

• Macaulay2
• K3Carpets

Cites Work

• Vanishing resonance and representations of Lie algebras
• Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
• Syzygies of canonical curves and special linear series
• Hilbert functions and Betti numbers in a flat family
• The canonical syzygy conjecture for ribbons
• Green's conjecture for the generic \(r\)-gonal curve of genus \(g\geq 3r-7\).
• Green's generic syzygy conjecture for curves of even genus lying on a \(K3\) surface
• Equations and syzygies of \(K3\) carpets and unions of scrolls
• Koszul modules and Green's conjecture
• Remarks on syzygies of \(d\)-gonal curves
• A Version of Green’s Conjecture in Positive Characteristic
• Degenerations of K3 surfaces in projective space
• New evidence for Green's conjecture on syzygies of canonical curves
• The Geometry of Syzygies
• Ribbons and Their Canonical Embeddings
• Clifford Indices of Ribbons
• Chen Lie algebras
• green's canonical syzygy conjecture for generic curves of odd genus
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