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