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at the origin of $f+x_{c+1}^2+\cdots+x_n^2$. Here $f$ is the normal form in $c$ variables $x,y,z$ of a simple singularity, a parabolic unimodal singularity, or- an exceptional unimodal singularity in Arnold's classification CITE{AGV}; for the- unimodal families the modulus is set to $0$. The normal forms are $A_k:x^{k+1}$;+ an exceptional unimodal singularity in Arnold's classification CITE{AGV} with the+ modulus set to $0$ for the unimodal families. The normal forms are $A_k:x^{k+1}$; $D_k:x^2y+y^{k-1}$; $E_6:x^3+y^4$; $E_7:x^3+xy^3$; $E_8:x^3+y^5$; $P_8:x^3+y^3+z^3$; $X_9:x^4+y^4$; $J_{10}:x^3+y^6$; $E_{12}:x^3+y^7$; $E_{13}:x^3+xy^5$; $E_{14}:x^3+y^8$;
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