How to find the chart around $(0,0)$ of $\{(z,w)\in\mathbb C\times \mathbb C: w^3= z^2(z^2-1)\}$? For $f(z,w)= w^3-z^2(z^2-1)$, in this case both $\frac{\partial f(z,w)}{\partial z}$ and $\frac{\partial f(z,w)}{\partial w}$ at $(0,0)$ vanishes. So the projection map does not become a chart—any hint to proceed with this?
2026-04-05 20:51:21.1775422281
Riemann surface $w^3= z^2(z^2-1)$
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