Algebraic approximation of germs of real analytic sets
Authors:
M. Ferrarotti, E. Fortuna and L. Wilson
Journal:
Proc. Amer. Math. Soc. 138 (2010), 15371548
MSC (2000):
Primary 14P15, 32B20, 32S05
Published electronically:
January 19, 2010
MathSciNet review:
2587437
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Abstract: Two subanalytic subsets of are equivalent at a common point, say , if the Hausdorff distance between their intersections with the sphere centered at of radius goes to zero faster than . In the present paper we investigate the existence of an algebraic representative in every equivalence class of subanalytic sets. First we prove that such a result holds for the zeroset of an analytic map when the regular points of are dense in . Moreover we present some results concerning the algebraic approximation of the image of a real analytic map under the hypothesis that .
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Additional Information
M. Ferrarotti
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I10129 Torino, Italy
Email:
ferrarotti@polito.it
E. Fortuna
Affiliation:
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, I56127 Pisa, Italy
Email:
fortuna@dm.unipi.it
L. Wilson
Affiliation:
Department of Mathematics, University of Hawaii, Manoa, Honolulu, Hawaii 96822
Email:
les@math.hawaii.edu
DOI:
http://dx.doi.org/10.1090/S0002993910102834
Received by editor(s):
January 9, 2009
Published electronically:
January 19, 2010
Additional Notes:
This research was partially supported by M.I.U.R. and by G.N.S.A.G.A
Communicated by:
Daniel Ruberman
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
