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We present preliminary results from an ongoing calculation to determine thecurvature of the chiral phase transition line in the chiral limit along thelight-light, light-strange and strange-strange chemical potential directions.We do this by studying the appropriate $\mu$-derivatives of the chiralcondensate as a function of the quark mass and comparing them to the scalingpredictions of $3d$-$O(N)$ theory. We work at a fixed lattice spacing,$N_\tau=6$ and at four different quark masses $m_\pi\approx$ 140, 110, 90 and80 MeV. For the light quark curvature, we obtain a value0.03$\leqslant\kappa_{ll}\leqslant$0.11. We also find that both strange andlight-strange curvatures are around an order of magnitude smaller. Currently,the light-strange curvature is the least constrained curvature and could haveeither sign, though our results seem to prefer a slightly negative value.

The curvature of the chiral phase transition line for small values of $\mu_B$