@inproceedings{Aprodu2001OnTV,
title={On the vanishing of higher syzygies of curves},
author={Marian Aprodu},
year={2001}
}

Marian Aprodu

Published 2001

One of the remarkable results of Segre’s, quoted in [AC] as Theorem 0.2, states that generic k-gonal curves have distinguished nodal models lying on the Hirzebruch surface Σ1, in such a way that minimal pencils are given by the ruling. Since there exist several results relating Koszul cohomology of a surface to the Koszul cohomology of curves which lie on it, it seems natural to make use of this very geometric context to verify some cases of Green’s conjecture. As exemplified by the main result… CONTINUE READING

Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension

R. Lazarsfeld

Invent . Math . • 1993

Loose , On the graded Betti numbers of plane algebraic curves

F. Lo

Proc . Int . Congr . Math . , Kyoto / Japan • 1990

A standard basis approach to syzygies of canonical curves

F.-O. Schreyer

Green ’ s conjecture for general pgonal curves of large genus , Algebraic curves and projective geometry , Trento , 1988 , Lecture Notes in Math . • 1989

The Clifford dimension of a projective curve

H. Lange, G. Martens, F.-O. Schreyer

1989

Koszul cohomology and the geometry of projective varieties

M. Green

J. Diff. Geom • 1984

Lazarsfeld, The nonvanishing of certain Koszul cohomology groups

R. M. Green

J. Diff. Geom • 1984

The nonvanishing of certain Koszul cohomology groups

M. Green, R.

J . Diff . Geom . • 1984

Koszul cohomology and the geometry of projective varieties II

R. Lazarsfeld

J . Diff . Geom .

Lazarsfeld , On the projective normality of complete linear series on an algebraic curve