Geodesic
Finiteness problems on Nash manifolds and Nash sets
Journal of the European Mathematical Society, Tome 16 (2014) no. 3, pp. 537-570.

Voir la notice de l'article provenant de la source EMS Press

We study here several finiteness problems concerning affine Nash manifolds M and Nash subsets X. Three main results are: (i) A Nash function on a semialgebraic subset Z of M has a Nash extension to an open semialgebraic neighborhood of Z in M, (ii) A Nash set X that has only normal crossings in M can be covered by finitely many open semialgebraic sets U equipped with Nash diffeomorphisms (u1​,...,um​):U→Rm such that U∩X={u1​⋯ur​=0}, (iii) Every affine Nash manifold with corners N is a closed subset of an affine Nash manifold M where the Nash closure of the boundary ∂N of N has only normal crossings and N can be covered with finitely many open semialgebraic sets U such that each intersection N∩U={u1​≥0,...ur​≥0} for a Nash diffeomorphism (u1​,...,um​):U→Rm.
DOI : 10.4171/jems/439
Classification : 14-XX, 00-XX, 32-XX, 58-XX
Keywords: Finiteness, Nash functions and Nash sets, semialgebraic sets, Nash manifolds with corners, extension, normal crossings at a point, normal crossings divisor 
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     author = {Jos\'e F. Fernando and Jos\'e Manuel Gamboa and Jes\'us M. Ruiz},
     title = {Finiteness problems on {Nash} manifolds and {Nash} sets},
     journal = {Journal of the European Mathematical Society},
     pages = {537--570},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2014},
     doi = {10.4171/jems/439},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/439/}
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José F. Fernando; José Manuel Gamboa; Jesús M. Ruiz. Finiteness problems on Nash manifolds and Nash sets. Journal of the European Mathematical Society, Tome 16 (2014) no. 3, pp. 537-570. doi : 10.4171/jems/439. http://geodesic.mathdoc.fr/articles/10.4171/jems/439/

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