Algebraic Montgomery-Yang problem and cascade conjecture

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 …

代数 Montgomery-Yang 问题与光滑阻碍

Algebraic Montgomery-Yang problem and smooth obstructions

本文利用 Donaldson 对角化定理和 Heegaard Floer 校正项等光滑 4-流形工具，排除特定四奇点情形并识别满足 orbifold BMY 不等式但被光滑条件阻碍的无穷多奇点类型，推进了代数 Montgomery-Yang 问题的研究。