Kodaira dimension
The Enriques–Kodaira classification classifies algebraic surfaces: coarsely by Kodaira dimension, then in more detail within a given Kodaira dimension. To give some simple examples: the product P1 × "X" has Kodaira dimension formula_5 for any curve "X"; the product of two curves of genus 1 (an abelian surface) has Kodaira dimension 0; the product of a curve of genus 1 with a curve of genus at least 2 (an elliptic surface) has Kodaira dimension 1; and the product of two curves of genus at least 2 has Kodaira dimension 2 and hence is of general type.