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Non-Trivial Examples of Real Isolated Singularity at the Origin

机译：原点上实数孤立奇点的非平凡例子

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The existence of nontrivial examples of real polynomial (or differentiable) maps with isolated singularity at the origin has been shown in most dimensions. Church and Lamotke used a result by Looijenga to prove the existence of such examples. Church and Timourian have shown when such examples exist. However, such examples are rare. Milnor, in his book 'Singularities of Complex Hypersurfaces', has cited an example by Kuiper of an isolated singularity at the origin which does not come from a complex one. A'Campo has presented another example in one of his papers. The objective here is to survey all these results and examples and bring them together in one article. In Section One, we introduce basic definitions and properties. Section Two is reserved for the results by Church and Lamotke, Church and Timourian, Looijenga and Milnor; while in Section Three, we state the only known explicit examples.

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