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We investigate the behavior of the pseudo-critical temperature of $N_f = 2+1$QCD as a function of a static magnetic background field for different values ofthe pion mass, going up to $m_\pi \simeq 660$ MeV. The study is performed bylattice QCD simulations, adopting a stout staggered discretization of thetheory on lattices with $N_t = 6$ slices in the Euclidean temporal direction;for each value of the pion mass the temperature is changed moving along a lineof constant physics. We find that the decrease of $T_c$ as a function of $B$,which is observed for physical quark masses, persists in the whole exploredmass range, even if the relative variation of $T_c$ appears to be a decreasingfunction of $m_\pi$, approaching zero in the quenched limit. The location of$T_c$ is based on the renormalized quark condensate and its susceptibility;determinations based on the Polyakov loop lead to compatible results. On thecontrary, inverse magnetic catalysis, i.e. the decrease of the quark condensateas a function of $B$ in some temperature range around $T_c$, is not observedwhen the pion mass is high enough. That supports the idea that inverse magneticcatalysis might be a secondary phenomenon, while the modifications induced bythe magnetic background on the gauge field distribution and on the confiningproperties of the medium could play a primary role in the whole range of pionmasses

QCD phase diagram in a magnetic background for different values of the pion mass