Related papers: Cliff-wall surgery and vanishing of basic phase fu…

This paper is cancelled

This paper has been withdrawn by the author due to an error in the proof of Theorem 1.

This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

I withdraw my paper from arXiv because there is a technical error in the proof of Theorem 1.1. And because of this error, all the results in the paper are untrue. I am very sorry for this.

This paper has been withdrawn by the author, due to an important sign error in Eqn. 2.

This paper is withdrawn due to some gaps in the proof

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).

The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.

This submission has been withdrawn by arXiv administrators because it is incomplete and thus violates arXiv policy.

This paper is withdrawn.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

Paper withdrawn, see math-ph/0505072

This paper has been withdrawn.

This paper has been withdrawn by the author due to a errors in figure 3,4

This paper has been withdrawn by the author due to a crucial argument error at p.10.

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author. It is not true that plt blow-up of toric singularity is toric (in dimension 3 too) and the first main theorem is incorrect also. The error is in deformation argument. I am grateful to Ivan…

This paper has been withdrawn due to a error in Theorem 3.1.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

The general structure of the paper should be remaid. Hence author removed this paper from arXiv.

Paper withdrawn due to errors.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