相关论文: Combinatorial shifting and graded Betti numbers

This paper is withdrawn.

This paper has been withdrawn by the authors, due a crucial error in Sec. 3.

This paper has been withdrawn by the authors, due to the discovery of paper 0201028 which predates it and contains most of it's results.

This paper has been withdrawn by the author due to a crucial mistakes.

This paper has been withdrawn while the author verifies the literature.

This paper has been withdrawn by the author.

The paper is being withdrawn since the results are incorporated in paper arxiv.org/abs/math.AG/0306195.

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This paper has been withdrawn due to an error, and no further revisions will be made.

This paper has been withdrawn. The contents of this paper can now be found in 0907.3000, which combines the erstwhile 0901.2981 and 0901.2982 in a somewhat compact form.

This paper has been withdrawn.

This paper has been withdrawn by the author. It will be replaced, substantially modified, by sections of the author's completed PhD thesis.

This paper has been withdrawn.

This paper has been withdrawn.

This paper has been withdrawn.

This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…

This paper was withdrawn by the authors.

This paper has been withdrawn by the authors, as it was combined with "Conformally invariant energies of knots I" (math/0409396) to be "Conformally invariant energies of knots" which has replaced the former.

This paper has been withdrawn due to non-clearness of some technical points, as well as lack of a reasonable statement of quantization conjecture.