Chains on the Eggers tree and polar curves
Chains on the Eggers tree and polar curves
If B is a branch at O\in\mathbb{C}^2 of a holomorphic curve, a Puiseux parametrisation y=\psi(x) of B determines "pro-branches" defined over a sector |\mathrm{arg} x-\alpha| < \varepsilon . The exponent of contact of two pro-branches is the (fractional) exponent of the first power of x where they differ. We first …