On hereditarily rational functions
arXiv:1211.6681
Abstract
In this paper, we give a short proof of a theorem by Kollár on hereditarily rational functions. This is an answer to his appeal to find an elementary proof which does not rely so much on resolution of singularities. Our approach does not make use of desingularization techniques. Instead, we apply a stronger version of the Łojasiewicz inequality. Moreover, this allows us to sharpen Kollár's theorem.
5 pages