  We present recent results on the critical and pseudo-critical temperatures in
(2+1)-flavor QCD with a physical strange quark mass and two degenerate light
quark masses extrapolated to the chiral limit and tuned to the physical value,
respectively. We furthermore discuss implication of the observed low chiral
phase transition temperature, Tc0=132_{-6}^{+3} MeV, for the structure of
cumulants of conserved charge fluctuations at vanishing baryon chemical
potential and consequences for the possible location of the QCD critical
endpoint in the QCD phase diagram at non-zero baryon chemical potential.
