Related papers: On the Koszul Betti numbers in positive characteri…

Paper withdrawn due to errors. Revised version may or may not appear in the future.

The paper has been withdrawn due to numerical error.

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.

This paper has been withdrawn by the author due to a error in attachment of source file.

The paper was retracted.

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

This paper has been withdrawn by the authors because the paper is largely revised and improved.

This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.

This paper has been withdrawn by the author due to an error in the proof of Theorem 6.

We prove a strong vanishing result for finite length Koszul modules, and use it to derive Green's conjecture for every g-cuspidal rational curve over an algebraically closed field k with char(k) = 0 or char(k) >= (g+2)/2. As a consequence,…

This paper has been withdrawn by the author, due to a crucial error in page 5.

This paper has been withdrawn by the authors due to an error in Section 7.

This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.

The paper is withdrawn due to mistakes in the proofs for Proposition 1.2 and Theorem 2.2.

The paper has benn withdrawn because the computation of the external virial contains an error which invalidate the main result.

The methods used to prove the main result must be incorrect, as they can be used to arrive at a contradiction with previously known results. Thus the paper was withdrawn.

This paper has been withdrawn by the author due to a serious gap in the proof of the main theorem.

This paper has been withdrawn by the authors due to some fatal errors in the analysis.

This paper has been withdrawn by the authors, due a crucial error in the proof of the main theorem.

The paper is withdrawn. The proof has an error and it requires a different approach.