There are different views about how Calabi-Yau variety should be defined. A characterization that is most appropriate for many applications of these spaces is to define them as compact Kaehler varieties with vanishing first Chern class. Sometimes stricter definitions are adopted, but these lead to the exclusion of certain degenerate cases, such as the product of a K3 surface with an elliptic curve, or triple products of elliptic curves, that really should not excluded.

There are different views about how Calabi-Yau varieties should be defined. A characterization that is most appropriate for many applications of these spaces is to define them as compact Kaehler varieties with vanishing first Chern class. Sometimes stricter definitions are adopted, but these lead to the exclusion of certain degenerate cases, such as the product of a K3 surface with an elliptic curve or the triple products of elliptic curves, that really should not be excluded.