  We present here the results from an ongoing determination of the critical
quark mass in simulations of (2+1)-flavor QCD with an imaginary chemical
potential. Studies with unimproved actions found the existence of a critical
quark mass value at which the crossover transition ends on a second order phase
transition and becomes first order for smaller values of the quark mass for the
case of both vanishing and imaginary chemical potential. We use the Highly
Improved Staggered Quark (HISQ) action and perform calculations in the
Roberge-Weiss (RW) plane, where the value of the critical mass is expected to
be largest. The lowest quark mass value used in our simulation corresponds to
the pion mass $m_\pi$, down to $40$ MeV. Contrary to calculations performed
with unimproved actions we find no evidence for the occurrence of first order
transitions at the smallest quark mass values explored so far. Moreover we also
show that the chiral observables are sensitive to the RW transition. Our
results also indicate that the RW transition and chiral transition could
coincide in the chiral limit.
