Rokhlin's complex orientations of a real algebraic curve dividing
its complexification
are generalized to real algebraic surfaces. First, the notion of type
of a real
allegoric curve is generalized. In place of two type (curves dividing
and non-dividing
their complexifications) we consider three types: I absolute, I relative
and II.
A surface belongs to type I absolute, if its real part is zero-homologous
modulo 2
in the complexification. A surface is of type I relative, if its real
part is homologous
modulo 2 to the class of hyperplane section. In other cases it is of
type II. For a
surface of type I absolute a pair of opposite to each other orientations
of the set
of real points is defined. For a surface of type I relative, the set
of real points
is oriented in the complement of a hyperplane section. At the end of
the paper similar
Spin- and Pin- structures are defined for surfaces of type I absolute
and I relative,
respectively.