Remarks on syzygies of $d$-gonal curves

Details Remarks on syzygies of $d$-gonal curves Remarks on syzygies of $d$-gonal curves

2004-12-07

arxiv.org/abs/math/0412134v3

Mathematics

Algebraic Geometry

final version to appear in Math. Res. Lett

Scientific paper

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.

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