Marian Aprodu

Green’s conjecture for curves on arbitrary K 3 surfaces

Green’s conjecture predicts than one can read off special linear series on an algebraic curve, by looking at the syzygies of its canonical embedding. We extend Voisin’s results on syzygies of K 3 sections, to the case of K 3 surfaces with arbitrary Picard lattice. This, coupled with results of Voisin and Hirschowitz–Ramanan, provides a complete solution to Green’s conjecture for smooth curves on arbitrary K 3 surfaces.

Remarks on syzygies of d-gonal curves

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

Green-Lazarsfeld's conjecture for generic curves of large gonality

d

On the vanishing of higher syzygies of curves. II

-gonal stratum of curves

Green-Lazarsfeld gonality conjecture for a generic curve of odd genus

X

A CLASS OF HARMONIC SUBMERSIONS AND MINIMAL SUBMANIFOLDS

with

Holomorphic vector bundles on primary Kodaira surfaces

d<[g_X/2]+2

Moduli spaces of vector bundles over ruled surfaces

. By the same method, we verify the Green-Lazarsfeld conjecture for any curve of odd genus and maximal gonality. The proof invokes Voisins solution to the generic Green conjecture as a key argument.

Non-vanishing for Koszul cohomology of curves

We use Greens canonical syzygy conjecture for generic curves to prove that the Green–Lazarsfeld gonality conjecture holds for generic curves of genus g, and gonality d, if g/3<d<[g/2]+2. To cite this article: M. Aprodu, C. Voisin, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Stable rank-2 vector bundles over ruled surfaces

The present paper is related to a conjecture made by Green and Lazarsfeld concerning 1-linear syzygies of curves embedded by complete linear systems of sufficiently large degrees. Given a smooth, irreducible, complex, projective curve