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arXiv · 2012.13355

Algebraic Montgomery-Yang problem and cascade conjecture

DongSeon Hwang
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Abstract

The conjecture called algebraic Montgomery-Yang problem is still open for rational $\mathbb{Q}$-homology projective planes with cyclic quotient singularities having ample canonical divisor. All known such surfaces have a special birational behavior called a cascade. In this note, we establish algebraic Montgomery-Yang problem assuming the cascade conjecture, which claims that every rational $\mathbb{Q}$-homology projective planes with quotient singularities having ample canonical divisor admits a cascade.

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DongSeon Hwang. 2020-12-24. Algebraic Montgomery-Yang problem and cascade conjecture. https://arxiv.org/abs/2012.13355

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