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On the pythagoras numbers of real analytic set germs.


Fernando Galván, José Francisco and Ruiz Sancho, Jesús María (2005) On the pythagoras numbers of real analytic set germs. Bulletin de la Société Mathématique de France , 133 (3). pp. 349-362. ISSN 0037-9484

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We Show that (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number 2 if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive semidefinite analytic function germs.

Item Type:Article
Uncontrolled Keywords:Pythagoras number; sum of squares; M. Artin’s approximation.
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15159

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