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The Arctic region is undergoing dramatic transformation. With the melting of ice, the circumpolar region is subject to increasing forces of globalization, and navigating through the Northwest and the Northeast passages is rapidly emerging as a practical and commercial position. How can science calculate and assess the scale of change in this geographic space ? To what extent are the Native populations listened to and act as active participants in decision-making concerning the Arctic ? What is the present state of Arctic governance ? What role can be played by the others countries ?

Projective geometry is a very classical part of mathematics and one might think that the subject is completely explored and that there is nothing new to be added. But it seems that there exists no book on projective geometry which provides a systematic treatment of morphisms. We intend to fill this gap. It is in this sense that the present monograph can be called modern. The reason why morphisms have not been studied much earlier is probably the fact that they are in general partial maps between the point sets G and G, noted ' 9 : G -- ~ G', i.e. maps 9 : D -4 G' whose domain Dom 9 := D is a subset of G. We give two simple examples of partial maps which ought to be morphisms. The first example is purely geometric. Let E, F be complementary subspaces of a projective geometry G. If x E G \ E, then g(x) := (E V x) n F (where E V x is the subspace generated by E U {x}) is a unique point of F, i.e. one obtains a map 9 : G \ E -4 F. As special case, if E = {z} is a singleton and F a hyperplane with z tf. F, then g: G \ {z} -4 F is the projection with center z of G onto F.