The gonality conjecture on syzygies of algebraic curves of large degree

DOI10.1007/s10240-015-0072-2zbMath1342.14070arXiv1407.4445OpenAlexW2095520969WikidataQ56700157 ScholiaQ56700157MaRDI QIDQ897008

Robert Lazarsfeld, Lawrence Ein

Publication date: 16 December 2015

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.4445

zbMATH Keywords

Koszul cohomologygonalitysyzygycanonical curve

Mathematics Subject Classification ID

Divisors, linear systems, invertible sheaves (14C20) Special divisors on curves (gonality, Brill-Noether theory) (14H51)

Related Items (19)

Sums of squares and quadratic persistence on real projective varieties ⋮ Hermite Reciprocity and Schwarzenberger Bundles ⋮ \(S_n\)-equivariant sheaves and Koszul cohomology ⋮ A matryoshka structure of higher secant varieties and the generalized Bronowski's conjecture ⋮ Cubics in 10 variables vs. cubics in 1000 variables: Uniformity phenomena for bounded degree polynomials ⋮ New constructions of nef classes on self-products of curves ⋮ Universal secant bundles and syzygies of canonical curves ⋮ Fourier-Mukai transformation and logarithmic Higgs bundles on punctual Hilbert schemes ⋮ Asymptotic vanishing of syzygies of algebraic varieties ⋮ Extension groups of tautological bundles on symmetric products of curves ⋮ A LOWER BOUND FOR THE GONALITY CONJECTURE ⋮ Progress on Syzygies of Algebraic Curves ⋮ Singularities and syzygies of secant varieties of nonsingular projective curves ⋮ Some remarks on the work of Lawrence Ein ⋮ Tangent developable surfaces and the equations defining algebraic curves ⋮ On the vanishing of weight one Koszul cohomology of abelian varieties ⋮ Computing graded Betti tables of toric surfaces ⋮ Linear syzygies of curves with prescribed gonality ⋮ Koszul modules and Green's conjecture

Cites Work

• \(S_n\)-equivariant sheaves and Koszul cohomology
• Asymptotic syzygies of algebraic varieties
• Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
• Koszul cohomology and the geometry of projective varieties. II
• On the projective normality of complete linear series on an algebraic curve
• Green-Lazarsfeld's conjecture for generic curves of large gonality.
• Green's generic syzygy conjecture for curves of even genus lying on a \(K3\) surface
• green's canonical syzygy conjecture for generic curves of odd genus
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