The presence of не, negating a transitive verb has caused the direct object to take the genitive case. Unfortunately, this is not a hard and fast rule, it could just as well be in the accusative.
http://www.study-languages-online.com/russian-genitive-case.html ... item 4.
As discussed above, this is not entirely true. Both "Я не вижу синюю машину" and "Я не вижу синей машины" are legitimate sentences. In my intuitive feeling, the first one talks about a specific blue car and has some context, and the second one talks about any blue car and is a general sentence without certain context.
This link does not really look into this detail. I think the suggestion that "тут" has an influence might have something in it as well.
After a lot of saying both out loud, the most I can say from my own feeling:
Я не вижу тут синюю машину sounds like I don't see the/that blue car here (some sort of context has to be there, somebody's car, or someone pointed out, look, there's a blue car that has to be there)
Я не вижу тут синей машины sounds like it has less context, I don't see any/a blue car. Nobody said it has to be there, I just looked and saw, say, all the rainbow colours but blue.
I might be wrong, native speaker problems x)
Could be, but this "sloppiness" happens not only with "I don't see" (related to "there is no") but also with "I don't want".
Example: Я не хочу молоко (Acc.). Я не хочу молока (Gen).
The second one is much more common, in my explanation that is because you're saying "I don't want (any) milk now, I'm not thirsty" rather than "I don't want this/the milk, that was offered just now."
I hope more people reply here to clarify this :)
ah, right this pattern has appeared on duo several times before but not with negative sentences. That is probably why it is confusing. The genitive technically means: "(some) of the". It has the same structure as French "du thé". and with "нет" it means "none of the" but one can also use genitive without нет.
Хочу чай / не хочу чай: it's tea I want (don't want) Хочу чаю (чая) / не хочу чаю (чая): I want (don't want) some tea and probably the last sentence is better translated as I don't want any tea.
I'm curious about something. Wouldn't this be an example of the failure of Russian "question words"? I mean, for "синяя машина" wouldn't this be a "Кого? Что?" which would leave you with "синюю машину" instead of "синей машины"? And if it isn't "Кого? Что?", how would one have known?
I think in this sentence the genitive case applies to the adjective "blue" because it means that there are no cars belonging to the category OF color blue (in the place where the person who talks is looking for one).
I hope I'm making myself clear (English is not my native language).