相关论文: A note on symplectic rational blow--downs

This paper was withdrawn by the authors due to significant new findings. A new paper on the same topic has been submitted as physics/0310159.

The authors have found an error in their argument, so this paper is withdrawn.

We study F-blowups of non-F-regular normal surface singularities. Especially the cases of rational double points and simple elliptic singularities are treated in detail.

This paper has been withdrawn by the author due to a crucial error related with the consideration of regular points

We prove that smooth quartic threefolds are symplectically irrational, i.e., cannot be related to projective space by a series of symplectic blow-ups, blow-downs, and deformations. This implies that they are algebraically irrational,…

We completely classify redundant blow-ups appearing in the theory of rational surfaces with big anticanonical divisor due to Sakai. In particular, we construct a rational surface with big anticanonical divisor which is not a minimal…

In this article we construct a new family of simply connected symplectic 4-manifolds with $b_2^+ =1$ and $c_1^2 =2$ which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a…

This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).

The normal connected sum construction of Gompf and the rational blowing-down technique of Fintushel - Stern are important tools in constructing symplectic 4-manifolds. In some cases, the 4-manifolds created this way are of Kahler type. In…

We show that there is a complex structure on the symplectic 4-manifold $W_{4, k}$ obtained from the elliptic surface E(4) by rationally blowing down $k$ sections for $2\le k\le 9$. And we interpret it via ${\mathbb Q}$-Gorenstein smoothing.…

This work is motivated by mathematical questions arising in differential equation models for autocatalytic reactions. In particular, this paper answers an open question posed by Guckenheimer and Scheper [SIAM J. Appl. Dyn. Syst. 10-1…

This has been withdrawn by the authors.

The Milnor fibre of a $\mathbb{Q}$-Gorenstein smoothing of a Wahl singularity is a rational homology ball $B_{p,q}$. For a canonically polarised surface of general type $X$, it is known that there are bounds on the number $p$ for which…

In a previous work, we proved that each minimal symplectic filling of any oriented lens space, viewed as the singularity link of some cyclic quotient singularity and equipped with its canonical contact structure, can be obtained from the…

In this paper we present a method for extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimension,…

This paper has been withdrawn by the authors due to the paper is far from complishment.

This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0511016) in a clearer way.

This paper has been withdrawn by the author due to incomplete interpretation for the results.

This paper was withdrawn (temporarily?) by the author since an error needs to be corrected.

This paper has been withdrawn by the author due to essential mistakes in some previous versions.