The genitive may be used instead of the accusative to express the direct object of a negated verb. The foreign student needs to know when one case or the other is obligatory or strongly preferred, but should also be aware that there are many instances where the question is finely balanced and either case might be acceptable to a native-speaker.
Note: there is no question of a genitive object being used if the negated verb is one which, when it is used affirmatively, governs the dative or instrumental case. Thus in the statement I am not interested in music the noun music would be rendered by an instrumental form (я нe интeрeсуюсь музыкой) just as it would if the verb интeрeсовaтъся were not negated. Only verbs which, when affirmative, govern the accusative case may govern a direct object in the genitive when they are negated.
Note: there is no question of a genitive object being used if the negated verb is one which, when it is used affirmatively, governs the dative or instrumental case. Thus in the statement I am not interested in music the noun music would be rendered by an instrumental form (я нe интeрeсуюсь музыкой) just as it would if the verb интeрeсовaтъся were not negated. Only verbs which, when affirmative, govern the accusative case may govern a direct object in the genitive when they are negated.