Lefschetz hyperplane theorem

The Lefschetz hyperplane theorem is a fundamental result in algebraic geometry and topology that relates the topology of a projective variety to that of its hyperplane sections. Specifically, it provides information about the cohomology groups of a projective variety and its hyperplane sections. To state the theorem more formally: Let \(X\) be a smooth projective variety of dimension \(n\) defined over an algebraically closed field.