Varieties of general type seem too complicated to classify explicitly, even for surfaces. Nonetheless, there are some strong positive results about varieties of general type. For example, Enrico Bombieri showed in 1973 that the "d"-canonical map of any complex surface of general type is birational for every formula_23. More generally, Christopher Hacon and James McKernan, Shigeharu Takayama, and Hajime Tsuji showed in 2006 that for every positive integer "n", there is a constant formula_24 such that the "d"-canonical map of any complex "n"-dimensional variety of general type is birational when formula_25.