Remarks on syzygies of $d$-gonal curves

Abstract

We apply a degenerate version of a result due to Hirschowitz, Ramanan and Voisin to verify Green and Green-Lazarsfeld conjectures over explicit open sets inside each $d$-gonal stratum of curves $X$ with $d<[g_X/2]+2$. By the same method, we verify the Green-Lazarsfeld conjecture for any curve of odd genus and maximal gonality. The proof invokes Voisin's solution to the generic Green conjecture as a key argument.

final version to appear in Math. Res. Lett

References in corpus (2)

• Green-Lazarsfeld's Conjecture for Generic Curves of Large Gonality
• Green-Lazarsfeld's Gonality Conjecture for a Generic Curve of Odd Genus

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• Green's canonical syzygy conjecture for ribbons
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• Difference varieties and the Green-Lazarsfeld Secant Conjecture
• Explicit presentations of nonspecial line bundles and secant spaces
• Green's Conjecture for curves on rational surfaces with an anticanonical pencil
• A remark on the generic vanishing of Koszul cohomology
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• The Rank of Syzygies of Canonical Curves