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Nash equidimensionality theorem

Author(s): Masato Fujita
Journal: Proc. Amer. Math. Soc. 133 (2005), 363-367.
MSC (2000): Primary 14P20
Posted: September 2, 2004
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Abstract: Consider a Nash mapping of Nash subsets. After a finite number of Nash blowings-up, the Nash mapping induced from it has equidimensional fibers. The purpose of this short note is to show this Nash equidimensionality theorem.

References:

1.: M. Coste, M. Ruiz and M. Shiota. Uniform bounds on complexity and transfer of g lobal properties of Nash functions. J. reine angew. Math., 536:209-235, 2001. MR 2003c:14065
2.: A. Parusinski. Subanalytic functions. Trans. Amer. Math. Soc., 344(2):583-59 5, 1994. MR 94k:32006
3.: M. Shiota. Piecewise linearization of subanalytic functions. II. Real analytic and algebraic geometry (Trento, 1998), 247-307, Lecture Notes in Math., 1420, Springer, Berlin, 1990. MR 91m:32009


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