Quark mass dependence of a QCD critical point and structure of the Columbia plot

We study the quark-mass dependence of the QCD critical point at varying bare up/down quark masses with fixed strange quark mass. We explore the corresponding second-order critical surface in the three-dimensional Columbia plot and study the extension of the associated crossover hyperplane at real and imaginary baryon chemical potential. To this end, we employ a by now well-tested combination of lattice Yang--Mills theory and a (truncated) version of Dyson--Schwinger equations at $N_f=2+1$ quark flavours. We find evidence for a positive curvature of the second order surface at (large) real chemical potential and a crossover region for imaginary chemical potential. Our results support the notion of a tricritical point at finite chemical potential in the chiral limit.