No coalescence conjecture for image-contractible deformations

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Let f:(Cn,S)→(Cn+1,0)f:(\mathbb{C}^n,S)\to(\mathbb{C}^{n+1},0) be an A\mathscr{A}-finite germ, and let ftf_t be a one-parameter deformation of ff. The coalescence problem is the simultaneous occurrence of more than one instability and a contractible image of ftf_t.

No coalescence conjecture. The coalescence problem does not occur: a one-parameter deformation ftf_t cannot have more than one instability and satisfy

im⁡ft≃{∗}\operatorname{im} f_t\simeq\left\{*\right\}

at the same time.

The claim concerns the coalescence phenomenon for germs from Cn\mathbb{C}^n to Cn+1\mathbb{C}^{n+1} and is presented as an expected extension of the paper's coalescence results to all n>2n>2. Its resolution status is not specified in the source excerpt.

References

Primary source

R. Giménez Conejero, “Isotypical components of the homology of ICIS and images of deformations of map germs”, arXiv:2207.05196 (2025).

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