A short proof of a theorem of Camacho and Sad (Q1594953)

The author of this paper gives a short proof of a theorem of Camacho and Sad. The theorem says that any holomorphic vector field defined in a neighborhood of the origin in \(\mathbb{C}^2\) admits an invariant complex curve passing through \(0 \in \mathbb{C}^2\). Based on the reduction theory for the singularities of a vector field and on the index theory of a foliation at a singular point with respect to an invariant curve, the author considers the negativity of the intersection form on the components of the exceptional divisor of a sequence of blow-ups to get his proof of the above theorem.