Publication:
Analytic surface germs with minimal Pythagoras number

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2003
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
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.
Description
Erratum: Analytic surface germs with minimal Pythagoras number.Mathematische Zeitschrift. 250(2005)no. 4, 967-969
Keywords
Citation
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)
Collections