相关论文: On the Koszul Betti numbers in positive characteri…

Paper withdrawn. Replaced by by gr-qc/0212077 .

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

This paper has been withdrawn by the author due to a crucial error in several equations.

The paper has been withdrawn by change of content and some errors in the examples.

This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.

This paper has been withdrawn by the author due to a crucial error in equation (51).

This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

This paper has been withdrawn to allow publication elsewhere.

This paper is withdrawn. We found a mistake in Lemma 4.1

This paper is withdrawn from submission due to a critical error in the proof of main theorem.

This paper has been withdrawn by the authors due to some errors.

This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1

The paper is withdrawn due to some errors.

This paper has been withdrawn by the author due to a crucial error in one of equation in (3).

This paper is being withdrawn by the authors in order to correct some errors and also to introduce improved theoretical techniques.

Given a base point free linear system on an algebraic variety, many classes of singularities are stable under taking suitable members after enlarging the base field. We establish analogous results when the base ring is an excellent ring.

This paper has been withdrawn by the authors due to essential errors in Theorem 5.6.

Following the well-established terminology in commutative algebra, any (not necessarily commutative) finite-dimensional local algebra $A$ with radical $J$ will be said to be short provided $J^3 = 0$. As in the commutative case, also in…

This paper has been withdrawn by the author due to a crucial sign error in equation 2 and some mistake in Table 1 information. please let me for changing this information and updating this paper.

This paper has been withdrawn by the authors owing to a mistake in the proof of the basic lemma.