You would still have the same age, gender, personality, skin color, etc. and you would be able to speak at least one local language and would know basic information of the era and place. Your family, social standing, and such would be randomly picked.
I reckon if you could get there 10 years early you could probably prevent the entire thing. If you were capable of convincing some of the larger groups within the americas of the impending invasion, there were certainly people and resources enough to put together a small navy and start patrolling the eastern coast. Throw is some modern knowledge of firearms and metallurgy to help them develop some cannon, and Columbus never makes it to America.
Back in Europe people assume him lost at sea, and leave the atlantic untouched for another generation. With that much time to prepare, who knows how things play out.