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Analytic surface germs with minimal Pythagoras number

Fernando Galván, José Francisco (2003) Analytic surface germs with minimal Pythagoras number. Mathematische Zeitschrift, 244 (4). pp. 725-752. ISSN 0025-5874

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Abstract

We determine all complete intersection surface germs whose Pythagoras number is 2, and find that they are all embedded in R-3 and have the property that every positive semidefinite analytic function germ is a sum of squares of analytic function germs. In addition, we discuss completely these properties for mixed surface germs in R-3. Finally, we find in higher embedding dimension three different families with these same properties.

Item Type:Article
Additional Information:Erratum: Analytic surface germs with minimal Pythagoras number.Mathematische Zeitschrift. 250(2005)no. 4, 967-969
Uncontrolled Keywords:Positive Semidefinite Germs; Squares; Rings; Sums
Subjects:Sciences > Mathematics > Number theory
Sciences > Mathematics > Algebraic geometry
ID Code:15229
References:

Artin, M.: On the solution of analytic equations. Invent. Math. 5, 227–291 (1968)

Bochnak, J., Risler, J.-J.: Le th´eor`eme des z´eros pour les vari´et´es analytiques r´eelles de dimension 2. Ann. Sc. ´ Ec. Norm. Sup. 4e serie 8, 353–364 (1975)

Eisenbud, D.: Commutative Algebra with a View Toward Algebraic Geometry.NewYork Berlin Heidelberg: Springer Verlag, 1999

Fernando, J.F.: On the Pythagoras numbers of real analytic rings. J. Algebra 243,321–338 (2001)

Fernando, J.F.: Positive semidefinite germs in real analytic surfaces. Math. Ann.322(1), 49–67 (2002)

Fernando, J.F.: Sums of squares in real analytic rings. Trans.AMS 354(5), 1909–1919 (2002)

Fernando, J.F., Ruiz, J.M.: Positive semidefinite germs on the cone. Pacific J. Math. 205, 109–118 (2002)

de Jong, T., Pfister, G.: Local Analytic Geometry, Basic Theory and Applications. Advanced Lectures in Mathematics. Braunschweig/Wiesbaden: Vieweg, 2000

Harris, J.:Algebraic Geometry,AFirst Course. GraduateText in Math. 133. Berlin Heidelberg NewYork: Springer Verlag, 1992

Ruiz, J.M.: The Basic Theory of Power Series. Advanced Lectures in Mathematics. BraunschweigWiesbaden: Vieweg Verlag, 1993

Ruiz, J.M.: Sums of two squares in analytic rings. Math. Z. 230, 317–328 (1999)

Scheiderer, C.: On sums of squares in local rings. J. reine angew. Math. 540, 205–227 (2001)

Stanley, R.: Hilbert functions of gradded algebras. Adv. inMath. 28, 57–83 (1978)

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Last Modified:06 Feb 2014 10:19

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