The $T-\mu$ phase diagram of QCD is, both theoretically
and experimentally, still largely unknown.
On the theoretical side, lattice QCD is the only reliable
tool to investigate the region close to the $\mu=0$ axis.
I will present our determinations of the curvature of the chiral
pseudocritical line from $N_f=2+1$ lattice QCD at the physical point
as obtained by adopting different approaches.
I will directly compare the method of the analytic continuation
from imaginary chemical potential with the method of Taylor expansion.
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