Complex surfaces

In mathematics, particularly in algebraic geometry and complex geometry, a **complex surface** is a two-dimensional complex manifold. This means that it is a manifold that locally resembles \(\mathbb{C}^2\) (the two-dimensional complex space) and can therefore be studied using the tools of complex analysis and differential geometry. A complex surface has the following characteristics: 1. **Complex Dimension:** A complex surface has complex dimension 2, which means it has real dimension 4.