Analytic surface germs with minimal Pythagoras number
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.date.accessioned | 2023-06-20T16:51:13Z | |
| dc.date.available | 2023-06-20T16:51:13Z | |
| dc.date.issued | 2003 | |
| dc.description | Erratum: Analytic surface germs with minimal Pythagoras number.Mathematische Zeitschrift. 250(2005)no. 4, 967-969 | |
| dc.description.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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15229 | |
| dc.identifier.doi | 10.1007/s00209-003-0519-x | |
| dc.identifier.issn | 0025-5874 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/krjuhbn3kjn9thnl/fulltext.pdf | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57236 | |
| dc.issue.number | 4 | |
| dc.journal.title | Mathematische Zeitschrift | |
| dc.language.iso | eng | |
| dc.page.final | 752 | |
| dc.page.initial | 725 | |
| dc.publisher | Springer | |
| dc.relation.projectID | BFM2002-04797 | |
| dc.relation.projectID | HPRN-CT-2001-00271 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 511 | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Positive Semidefinite Germs | |
| dc.subject.keyword | Squares | |
| dc.subject.keyword | Rings | |
| dc.subject.keyword | Sums | |
| dc.subject.ucm | Teoría de números | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1205 Teoría de Números | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | Analytic surface germs with minimal Pythagoras number | |
| dc.type | journal article | |
| dc.volume.number | 244 | |
| dcterms.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) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 499732d5-c130-4ea6-8541-c4ec934da408 | |
| relation.isAuthorOfPublication.latestForDiscovery | 499732d5-c130-4ea6-8541-c4ec934da408 |