We explain how a natural geometric interpretation of Abel’s dilogarithm identity leads to new functional equations for hyperlogarithms, arising from the pencils of conics on del Pezzo surfaces. These del Pezzo hyperlogarithmic identities are new, natural higher-weight generalizations (up to weight six) of Abel’s weight-two identity. After briefly comparing them with the classical dilogarithm equation, we present a geometric approach that produces all hyperlogarithmic identities of a given weight from a single differential identity. This identity is itself related to the geometry of a torus quotient of a certain homogeneous space.