  We present the crossover line between the quark gluon plasma and the hadron
gas phases for small real chemical potentials. First we determine the effect of
imaginary values of the chemical potential on the transition temperature using
lattice QCD simulations. Then we use various formulas to perform an analytic
continuation to real values of the baryo-chemical potential. Our data set
maintains strangeness neutrality to match the conditions of heavy ion physics.
The systematic errors are under control up to $\mu_B\approx 300$ MeV. For the
curvature of the transition line we find that there is an approximate agreement
between values from three different observables: the chiral susceptibility,
chiral condensate and strange quark susceptibility. The continuum extrapolation
is based on $N_t=$ 10, 12 and 16 lattices. By combining the analysis for these
three observables we find, for the curvature, the value $\kappa = 0.0149 \pm
0.0021$.
