On hereditarily rational functions

Preprint English OPEN
Nowak, Krzysztof Jan (2012)
  • Subject: 14P05 | Mathematics - Algebraic Geometry
    arxiv: Mathematics::Algebraic Geometry

In this paper, we give a short proof of a theorem by Koll\'{a}r 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 \L{}ojasiewicz inequality. Moreover, this allows us to sharpen Koll\'{a}r's theorem.
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    [5] K.J. Nowak, A note on Bierstone-Milman-Pawlucki's paper ”Composite differentiable functions”, Ann. Polon. Math. 102 (3) (2011), 293-299.

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