Related papers: Green's Conjecture for the generic canonical curve

We consider the generic Green conjecture on syzygies of a canonical curve, and particularly the following reformulation thereof: {\it For a smooth projective curve $C$ of genus $g$ in characteristic 0, the condition ${\rm Cliff} C>l$ is…

We study the syzygies of canonical curves of genus $g\geq 3$ over an algebraically closed field $\mathbb{F}$ of characteristic $p>0$. We provide a new proof of generic Green's Conjecture for $p\geq\frac{g+4}{2}$. Using the techniques from…

We prove that two weakened forms of Green's conjectures for canonical curves are equivalent when the genus $g$ is odd.

Green's canonical syzygy conjecture asserts a simple relationship between the Clifford index of a smooth projective curve and the shape of the minimal free resolution of its homogeneous ideal in the canonical embedding. We prove the…

We use Green's 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 $g/3<d<[g/2]+2$.

Green's conjecture is proved for smooth curves C lying on a rational surface S with an anticanonical pencil, under some mild hypotheses on the line bundle L defined by C. Constancy of Clifford dimension, Clifford index and gonality of…

We prove the Geometric Syzygy Conjecture for generic canonical curves of even genus. This result extends Green's classical result on the generation of the ideal of a canonical curve by rank four quadrics to the highest linear syzygy group.

We establish Green's syzygy conjecture for classes of covers of curves of higher Clifford dimension. These curves have an infinite number of minimal pencils, in particular they do not verify a well-known Brill-Noether theoretic sufficient…

We prove the Green conjecture for generic curves of odd genus. That is we prove the vanishing $K_{k,1}(X,K_X)=0$ for $X$ generic of genus $2k+1$. The curves we consider are smooth curves $X$ on a K3 surface whose Picard group has rank 2.…

We show that Generic Green's conjecture holds for generic binary curves, through a detailed analysis of the family of scrolls containing fixed rational normal curves.

By analogy with Green's Conjecture on syzygies of canonical curves, the Prym-Green conjecture predicts that the resolution of a general level p paracanonical curve of genus g is natural. The Prym-Green Conjecture is known to hold in odd…

We study the syzygies of the canonical embedding of a ribbon $\widetilde{C}$ on a curve $C$ of genus $g \geq 1$. We show that the linear series Clifford index and the resolution Clifford index are equal for a general ribbon of arithmetic…

We show the geometric syzygy conjecture in positive characteristic. Specifically, if C is a general smooth curve of genus g defined over an algebraically closed field of characteristic p, then all linear syzygy spaces are spanned by…

Generalizing the well-known Green Conjecture on syzygies of canonical curves, Green and Lazarsfeld formulated in 1986 the Secant Conjecture predicting that a line bundle L of sufficiently high degree on a curve has a non-linear p-syzygy if…

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 K3 sections, to the case of K3 surfaces with…

In this note, we give a new proof of Voisin's theorem on Green's conjecture for generic curves of odd genus resembling the first two sections of "Universal Secant Bundles and Syzygies of Canonical Curves" by the author, and so avoiding the…

The Green-Lazarsfeld Secant Conjecture is a generalization of Green's Conjecture on syzygies of canonical curves to the cases of arbitrary line bundles. We establish the Green-Lazarsfeld Secant Conjecture for curves of genus g in all the…

We show that a small variant of the methods used by Voisin in her study of canonical curves leads to a surprisingly quick proof of the gonality conjecture of Green and the second author, asserting that one can read off the gonality of a…

In a first part of this paper, we prove constancy of the canonical graded Betti table among the smooth curves in linear systems on Gorenstein weak Fano toric surfaces. In a second part, we show that Green's canonical syzygy conjecture holds…

We exhibit approximately fifty Betti diagrams of free resolutions of rings of smooth, connected canonical curves of genera $9$-$14$ in prime characteristics between $2$ and $11$. Generic Green's conjecture is verified for genera $9$ and…