A QUICK GLANCE at the facts of George Balanchine’s life suggests that he was destined to be a great choreographer. Born in 1904, he studied at what was then the most important ballet academy in the world, the Imperial Theater School in St. Petersburg; in the ’20s, he made dances in Europe for what was then the most important company in the world, Diaghilev’s Ballets Russes; by midcentury, in the United States and with his own troupe, he would finish creating what is still probably the most important choreographic canon in the world, Balanchine’s ballets. But Jennifer Homans’s new biography