In what grammatical context is the genitive case obligatory with negated verbs in Russian, even when the direct object is typically accusative?

The genitive case becomes obligatory in Russian with negated transitive verbs when the direct object represents an abstract or uncountable noun, or when the negation encompasses the existence or availability of the object rather than a specific action performed upon it. Transitive verbs are verbs that take a direct object. Normally, a direct object would be in the accusative case. Negation involves adding 'не' (ne) to the verb, creating a negative statement. For instance, instead of saying 'Я вижу книгу' (Ya vizhu knigu) - 'I see the book' (accusative), if you negate it and emphasize the absence of seeing *anybooks, you'd say 'Я не вижу книги' (Ya ne vizhu knigi) - 'I don't see *anybook' (genitive). This is most common when talking about abstract concepts such as 'I don't have time' (У меня нет времени - U menya net vremeni) where 'времени' (vremeni - time) is in the genitive. However, if the direct object is specific and definite even with negation, the accusative case can still be used; this often emphasizes the action *notbeing performed on that specific item. For example, if you specifically did not read *this particularbook you might still say 'Я не читал эту книгу' (Ya ne chital etu knigu) (accusative) - 'I did not read *thisbook'. Thus, the choice between genitive and accusative with negated verbs depends on the specificity and countability of the object, and more importantly, on the speaker's intent to emphasize the absence of the object itself or the action performed upon it. If the object is abstract, uncountable, or if the absence of the object is emphasized, the genitive is obligatory.