# Links of singular points in complex hypersurfaces

Consider the canonical embedding of a sphere of radius $\varepsilon$, say $S_\varepsilon^3$ inside $\mathbb C^2$ as the set of pairs $(z,w)$ with $|z|^2+|w|^2=\varepsilon^2$, and the curve $X= \{(z,w):z^k + w^l =0\}$. Calculate the homology of the intersection $X\cap S_\varepsilon^3$ for as many values of $(k,l)$ as possible where $k,l>1$, with $\varepsilon$ of your liking.

1. Hint: ﻿Carry out some simple computations involving the modui of $z,w$ to embed such intersection in a (compact) surface.