Surface of general type

Summary

A surface of general type is an algebraic surface of Kodaira dimension $2$, the largest possible value. Its pluricanonical systems $\abs{nK}$ grow as fast as possible, quadratically in $n$. Most surfaces are of this type, for example all smooth surfaces of degree at least $5$ in $\mathbb{P}^3$. Unlike the other classes in the Enriques–Kodaira classification, they are not classified in detail. Their study centres on inequalities between invariants and on their moduli spaces.