There are two artists I know of with the name Picabia - Francis Picabia, a famous cubist, and Maria Picabia, who I am guessing might have been his daughter? The painting you've linked seems to be either a Francis Picabia, or a fake Francis Picabia.
I am in no way an expert on his works, but looking through the ones we have on our site, I don't see a good match either in terms of style or signature. I can't find one where the signature matches the fat lettering and the dot of the "i" inside the loop of the "P" like you have here. So I wonder if it's a fake, but that's just my amateur guess.
The people to contact would be the Picabia Committee, aka "Comité Picabia" in France. They have a site here:
For some interesting background reading, here is an article that discusses the crazy history of Picabia fakes and the contentious work of the Comité Picabia itself: http://www.artnet.com/Magazine/features … -16-02.asp
Sorry I don't have a better answer, but if you read that article you'll find that even the "experts" often don't have a clear answer on Picabia's paintings.
Good luck, and let us know what you find out!