RT Journal Article T1 Analytic surface germs with minimal Pythagoras number A1 Fernando Galván, José Francisco AB 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. PB Springer SN 0025-5874 YR 2003 FD 2003 LK https://hdl.handle.net/20.500.14352/57236 UL https://hdl.handle.net/20.500.14352/57236 LA eng NO 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, 1999Fernando, 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, 2000Harris, J.:Algebraic Geometry,AFirst Course. GraduateText in Math. 133. Berlin Heidelberg NewYork: Springer Verlag, 1992Ruiz, J.M.: The Basic Theory of Power Series. Advanced Lectures in Mathematics. BraunschweigWiesbaden: Vieweg Verlag, 1993Ruiz, 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) NO Erratum: Analytic surface germs with minimal Pythagoras number.Mathematische Zeitschrift. 250(2005)no. 4, 967-969 NO DGICYT DS Docta Complutense RD 15 may 2024