La place des surfaces K 3 dans la classification des surfaces. Appendice A. Structure de Hodge d’une surface complexe. Par Paul Gauduchon (pp. 39- 40). Appendice B: Surfaces complexes et orientation. Par Arnaud Beauville (pp. 41-43). (French) Zbl 0574.14032

Géométrie des surfaces K 3: modules et périodes, Sémin. Palaiseau 1981-1982, Astérisque 126, 29-43 (1985).
[For the entire collection see Zbl 0547.00019.]
The present note contains a short and very clear review of Kodaira classification of analytic surfaces (compact, connected, complex analytic varieties of dimension two).
The first appendix is devoted to a brief account about Hodge structure of a complex surface.
In the second appendix the following question is discussed: may an analytic surface M have another complex analytic structure, inducing on it the opposite orientation? The answer is affirmative: if this happens either M has a holomorphic map onto a curve whose fibres are projective lines, or both Chern numbers of M are zero, or M is of general type, with some restrictions on the Chern numbers \((c^ 2_ 1\geq c_ 2\) and \(c^ 2_ 1\) even).
Reviewer: C.Ciliberto


14J10 Families, moduli, classification: algebraic theory
14J25 Special surfaces
32J15 Compact complex surfaces
14J15 Moduli, classification: analytic theory; relations with modular forms
32G20 Period matrices, variation of Hodge structure; degenerations
32G13 Complex-analytic moduli problems


Zbl 0547.00019