P. P. Cuadrado

A reduction theorem for L\^e's conjecture

Let $\boldsymbol{n}=(n_1,n_2,n_3):(\mathbb{C}^2,0)\to(\mathbb{C}^3,0)$ be a holomorphic map germ admitting an injective representative. We prove that if $(d\boldsymbol{n})_0=0$, then $\mathrm{ord}_0(\boldsymbol{n})\in\{2,3,4\}$. This reduces L\^e's conjecture to excluding potential counterexamples $\boldsymbol{n}$ of o...