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a) We consider real analylic surfaces M (i.e. dim*M:2) in C2. Two such surfaces M, ft are called equivalent if they can be mapped into each olher by a mapping which is biholomorphic in the complex struc"ture of C2. Actually, we are concerned only with local equivalence which refers to the neighbourhood of a point pofM. One has to distinguish points p for which the tangent space T.M:V is a complex line (i.e. V:iV) and those for which Z is totally real (i.e. V)|V:(O)). Points of the second type are uninteresting since any 1wo surfaces near such points are locally equivalent. Interesting are only the so-called "exceptional points" which were considered already by E. Bishop []. They are characlerized as points p with a complex tangent while for every q€M in a neighborhood of p TuM is totally real. Near such points one finds holomorphic invariants. For example, in the nondegenerate case, whete also the quadralic approxirnalion at p has an exceptional point, one can introduce local coordinates (z,w)€Cz so that the surface is given by

Analytic surfaces in C^2 and their local hull of holomorphy