The problem of detecting the bifurcation set of polynomial mappings $\mathbb{C}^m \to \mathbb{ C}^k$, $m\ge 2$, $m\ge k\ge 1$, has been solved in the case$m=2$, $k=1$ only. Its solution, which goes back to the 1970s, involves thenon-constancy of the Euler characteristic of fibres. We provide a completeanswer to the general case $m= k+1 \ge 3$ in terms of the Betti numbers offibres and of a vanishing phenomenon discovered in the late 1990s in the realsetting.
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机译：解决了多项式映射$ \ mathbb {C} ^ m \ to \ mathbb {C} ^ k $，$ m \ ge 2 $，$ m \ ge k \ ge 1 $的分叉集的问题case $ m = 2 $，仅$ k = 1 $。它的解决方案可以追溯到1970年代，涉及纤维欧拉特性的非恒定性。对于一般情况$ m = k + 1 \ ge 3 $，我们提供了完整的答案，包括贝蒂数异常和1990年代后期在现实环境中发现的消失现象。
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