We investigate the electronic structure of the new family of kagome metals AV$_{3}$Sb$_{5}$ (A = K, Rb, Cs) using first-principles calculations. We analyze systematically the evolution of the van Hove singularities (vHss) across the entire family upon applied pressure and hole doping, specifically focusing on the two vHss closer to the Fermi energy. With pressure, these two saddle points shift away from the Fermi level. At the same time, the Fermi surface undergoes a large reconstruction with respect to the Sb bands while the V bands remain largely unchanged, pointing to the relevant role of the Sb atoms in the electronic structure of these materials. Upon hole doping, we find the opposite trend, where the saddle points move closer to the Fermi level for increasing dopings. All in all, we show how pressure and doping are indeed two mechanisms that can be used to tune the location of the two vHss closer to the Fermi level and can be exploited to tune different Fermi surface instabilities and associated orders.
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