 Enriques–Babbage theorem

The Enriques–Babbage theorem is a result in algebraic geometry concerning the classification of surfaces. Specifically, it relates to the structure of certain rational surfaces, particularly those that can be expressed in terms of their canonical divisors and the presence of particular types of curves on these surfaces. The theorem states that if \( S \) is a smooth minimal surface of general type, then there exists a relation pertaining to the canonical divisor \( K \) of the surface that can help classify it.