重数为二和三的环境同胚孤立超曲面
Ambiently homeomorphic isolated hypersurfaces of multiplicities two and three
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具体内容
稿件针对嵌入型Zariski重数猜想给出否定回答。作者构造了两个既约超曲面芽，它们环境同胚但重数分别为二和三，均具孤立奇点，位于维数可被八整除的公共复仿射空间中。摘要还称其定义函数芽拓扑右等价，并据此对Arnold余秩问题在环境拓扑等价意义下给出否定回答。材料仅提供摘要，未展开构造与验证细节。
- 构造环境同胚但重数为二与三的既约孤立超曲面芽。
- 两例位于维数可被八整除的公共复仿射空间。
- 同一例子否定Arnold余秩问题在环境拓扑等价下的版本。
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英文原始摘要
We give a negative answer to the embedded Zariski multiplicity conjecture. We construct two reduced hypersurface germs that are ambiently homeomorphic but have multiplicities two and three. Both have isolated singularities and lie in a common complex affine space of dimension divisible by eight. Their defining function germs are also topologically right equivalent, and the same examples answer Arnold's corank problem negatively for ambient topological equivalence.
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