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Considering a nonlinear charged black hole as a thermodynamics system, westudy the geometric description of its phase transitions. Using the formalismof geometrothermodynamics we show that the geometry of the space ofthermodynamic equilibrium states of this kind of black holes is related withinformation about thermodynamic interaction, critical points and phasetransitions structure. Our results indicate that the equilibrium manifold ofthis black hole is curved and that curvature singularities appear exactly atthose places where first and second order phase transitions occur.

Geometric description of the thermodynamics of a black hole with power Maxwell invariant source