On the complements of 3-dimensional convex polyhedra as polynomial images of R3
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.contributor.author | Ueno, Carlos | |
| dc.date.accessioned | 2023-06-19T14:57:42Z | |
| dc.date.available | 2023-06-19T14:57:42Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | Let K Rn be a convex polyhedron of dimension n. Denote S := RnK and let S be its closure. We prove that for n = 3 the semialgebraic sets S and S are polynomial images of 3. The former techniques cannot be extended in general to represent the semialgebraic sets S and S as polynomial images of n if n ≥ 4. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish GR | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/34574 | |
| dc.identifier.doi | 10.1142/S0129167X14500712 | |
| dc.identifier.issn | 0129-167X | |
| dc.identifier.officialurl | http://arxiv.org/pdf/1212.1815v3.pdf | |
| dc.identifier.relatedurl | http://arxiv.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/34962 | |
| dc.issue.number | 7 | |
| dc.journal.title | International journal of mathematics | |
| dc.language.iso | eng | |
| dc.page.initial | 1450071 | |
| dc.publisher | World Scientific | |
| dc.relation.projectID | MTM2011-22435 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512 | |
| dc.subject.keyword | Polynomial maps and images | |
| dc.subject.keyword | Complement of a convex polyhedra | |
| dc.subject.keyword | First and second trimming positions | |
| dc.subject.keyword | Dimension 3 | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | On the complements of 3-dimensional convex polyhedra as polynomial images of R3 | |
| dc.type | journal article | |
| dc.volume.number | 25 | |
| dcterms.references | M. Berger: Geometry. I & II. Universitext. Springer-Verlag, Berlin: 1987. J. Bochnak, M. Coste, M.F. Roy: Real algebraic geometry. Ergeb. Math. 36. Springer-Verlag, Berlin: 1998. J.F. Fernando: On the one dimensional polynomial and regular images of Rn . J. Pure Appl. Algebra XXX (2014, accepted), no. X, XXX–XXX. J.F. Fernando, J.M. Gamboa: Polynomial images of Rn . J. Pure Appl. Algebra 179 (2003), no. 3, 241–254. J.F. Fernando, J.M. Gamboa: Polynomial and regular images of R n. Israel J. Math. 153 (2006), 61–92. J.F. Fernando, J.M. Gamboa, C. Ueno: On convex polyhedra as regular images of Rn. Proc. London Math.Soc. (3) 103 (2011), 847–878. J.F. Fernando, C. Ueno: On the set of points at infinity of a polynomial image of Rn. Preprint RAAG (2011).arXiv:1212.1811 J.F. Fernando, C. Ueno: On complements of convex polyhedra as polynomial and regular images of Rn. Int. Math. Res. Not. IMRN XXX (2013, accepted), no. X, XXX–XXX. J.M. Gamboa: Reelle Algebraische Geometrie, June, 10th − 16th (1990), Oberwolfach.[R] T.R. Rockafellar: Convex analysis. Princeton Mathematical Series, 28. Princeton University Press, Princeton,N.J: 1970. C. Ueno: A note on boundaries of open polynomial images of R 2. Rev. Mat. Iberoam. 24 (2008), no. 3,981-988. C. Ueno: On convex polygons and their complements as images of regular and polynomial maps of R2. J.Pure Appl. Algebra 216, no. 11, 2436–2448. C. Ueno: Unbounded convex polygons as polynomial images of the plane. Preprint RAAG (2013).arXiv:1307.8341 G.M. Ziegler: Lectures on Polytopes. Graduate Texts in Mathematics 152. Springer-Verlag, New-York:1995 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 499732d5-c130-4ea6-8541-c4ec934da408 | |
| relation.isAuthorOfPublication.latestForDiscovery | 499732d5-c130-4ea6-8541-c4ec934da408 |
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