In general, the genitive case describes or defines. It is the case of 'quality', 'attribute', 'description', or 'kind'. It limits the meaning of a substantive .
Some prepositions require that the noun be in the genitive case.
To see if it is the Genitive of Possession, try substituting the word 'of' with ' belonging to ' or ' possessed by '. However, this use does not have to indicate actual, physical ownership of some property. It may be a broadly defined type of ownership. This is a very common use of the genitive. A possessive pronoun will often be used in the genitive case to show possession.