On the arithmetic of isotropic Del Pezzo surfaces of degree six

Let X be a Del Pezzo surface of degree six defined over Q that is a compactification of an isotropic algebraic torus T. Then X is isomorphic over a quadratic extension of Q, the so-called splitting-field, to the blowing up of three points in general position in the projective plane. Suppose that the splitting field is imaginary quadratic. Let H be a fixed multiplicative anticanonical height on X. We rephrase our main result, Theorem 3.2.2: As B tends to infinity the counting function card {P is an element of T(Q) \ H(P) less than or equal to B} behaves like CB (log B)(Pic) (X) (-) (1)(1 + o (1)). C is a constant that admits an interpretation a la Peyre. Our goal is to work out, with the example of X, a method that goes back to Schanuel and Peyre and has been recently revisited by Salberger. The importance of torsors to obtain a deeper insight in these type of problems has been taught to the author by Per Salberger, to whom the author is deeply indebted for his indispensable help. The author would also like to thank Daniel Coray for his concern about this work and his constant encouragement.