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I am searching for a reference about the classification of algebraic surfaces over an arbitrary algebraically closed field of characteristic zero. In the 1949 book "le superficie algebriche" by Enriques there is no clear reference about the base field, as he only mentions some "ordinary space". Is it any arbitrary characteristic zero field, or $\mathbb{C}$? If it is $\mathbb{C}$, could you recommend a reference for the general zero characteristic case?

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I guess that with "ordinary space" Enriques meant $\mathbb{C}$, as this was the base field usually considered by "classical" italian algebraic geometers.

Moreover, the so-called Lefschetz principle, that allows to extend most of the results to surfaces defined over an arbitrary algebraically closed field of characteristic $0$, was formulated and illustrated the first time only in 1953 (in S. Lefschetz's book Algebraic Geometry).

Concerning your second request, the book Algebraic Surfaces by L. Badescu contains the classification over algebraically closed fields of arbitrary characteristic.

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