代数 Montgomery-Yang 问题与光滑阻碍

Algebraic Montgomery-Yang Problem: the non-rational case and the del Pezzo case

Montgomery-Yang problem predicts that every pseudofree differentiable circle action on the 5-dimensional sphere has at most 3 non-free orbits. Using a certain one-to-one correspondence, Kollár formulated the algebraic version of the Montgomery-Yang problem: every projective surface $S$ with the second Betti number $b_2(S) = 1$ and with quotient singularities only has at most 3 singular points if its smooth locus $S^0$ is simply-connected. In a previous paper, we have confirmed the conjecture when $S$ has at least one non-cyclic quotient singularity. In this paper, we prove the conjecture eithe…

代数蒙哥马利 - 杨问题

The Algebraic Montgomery-Yang Problem

研究代数蒙哥马利 - 杨问题，通过结合唐纳森对角化定理与特殊自旋^c结构得到新的格理论约束，连同orbifold博戈莫洛夫 - 宫冈 - 丘不等式，完全解决该问题，即证明相关有理同调射影平面最多有三个奇点。

Algebraic Montgomery-Yang Problem: the noncyclic case

Montgomery-Yang problem predicts that every pseudofree differentiable circle action on the 5-dimensional sphere ${\mathbb S}^5$ has at most 3 non-free orbits. Using a certain one-to-one correspondence, Kollár formulated the algebraic version of the Montgomery-Yang problem: every projective surface $S$ with quotient singularities such that $b_2(S) = 1$ has at most 3 singular points if its smooth locus $S^0$ is simply-connected. In this paper, we prove the conjecture under the assumption that $S$ has at least one noncyclic singularity. In the course of the proof, we classify projective surfaces …

A note on the $\mathbb Z_2$-equivariant Montgomery-Yang correspondence

In this paper, a classification of free involutions on 3-dimensional homotopy complex projective spaces is given. By the $\mathbb Z_2$-equivariant Montgomery-Yang correspondence, we obtain all smooth involutions on $S^6$ with fixed-point set an embedded $S^3$.

A generalization of Montgomery-Yang correspondence

In this paper, we want to construct a one-to-one correspondence from the set of diffeomorphism classes of spin $d$-twisted homology $\mc P^3$ to the set of isotopy classes of the embedding from $S^3$ to $S^6$, which is a generalization of the Montgomery-Yang correspondence. Furthermore, we will apply this generalized correspondence to prove the existence of free involution on these $d$-twisted homology $\mc P^3$.

存在拓扑Bogomolov-Miyaoka-Yau不等式吗？

Is there a topological Bogomolov--Miyaoka--Yau inequality?

本文的目的是考虑Bogomolov-Miyaoka-Yau不等式在可微轨道上的一个可能的推广。该扩张与Montgomery-Yang关于5-球面上的圆作用的问题有关，也与Seifert纤维3-流形的H-协边性有关。还讨论了与射影平面具有相同有理同调的商奇点代数曲面的相关性质。最后，我们给出这样的例子，这是双有理的射影平面，但有足够的标准类。