On the Set of Points at Infinity of a Polynomial Image of Rn
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.contributor.author | Ueno, Carlos | |
| dc.date.accessioned | 2023-06-19T13:27:51Z | |
| dc.date.available | 2023-06-19T13:27:51Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | In this work we prove that the set of points at infinity of a semialgebraic set that is the image of a polynomial map is connected. This result is no longer true in general if is a regular map. However, it still works for a large family of regular maps that we call quasi-polynomial maps. | |
| 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.sponsorship | GAAR Grupos | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/28337 | |
| dc.identifier.doi | 10.1007/s00454-014-9620-7 | |
| dc.identifier.issn | 0179-5376 | |
| dc.identifier.officialurl | http://arxiv.org/pdf/1212.1811v3.pdf | |
| dc.identifier.relatedurl | http://link.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33776 | |
| dc.issue.number | 4 | |
| dc.journal.title | Discrete & computational geometry | |
| dc.language.iso | eng | |
| dc.page.final | 611 | |
| dc.page.initial | 583 | |
| dc.publisher | Springer | |
| dc.relation.projectID | MTM2011-22435 | |
| dc.relation.projectID | UCM 910444 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Polynomial and regular maps and images | |
| dc.subject.keyword | Quasi-polynomial maps | |
| dc.subject.keyword | Set of points at infinity | |
| dc.subject.keyword | Connectedness. | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On the Set of Points at Infinity of a Polynomial Image of Rn | |
| dc.type | journal article | |
| dc.volume.number | 52 | |
| dcterms.references | []BCR J. Bochnak, M. Coste, M.F. Roy: Real algebraic geometry. Ergeb. Math. 36, Springer-Verlag, Berlin: 1998. []F J.F. Fernando: On the one dimensional polynomial and regular images of Rn. J. Pure Appl.Algebra 218 (2014), no. 9, 1745–1753. []FG1 J.F. Fernando, J.M. Gamboa: Polynomial images of Rn. J. Pure Appl. Algebra 179 (2003), no. 3,241–254. []FG2 J.F. Fernando, J.M. Gamboa: Polynomial and regular images of Rn. Israel J. Math. 153 (2006),61–92. []FG3 J.F. Fernando, J.M. Gamboa: On the irreducible components of a semialgebraic set. Internat. J.Math. 23 (2012), no. 4, 1250031 (40 pages). []FGU1 J.F. Fernando, J.M. Gamboa, C. Ueno: On convex polyhedra as regular images of Rn. Proc. Lond.Math. Soc. (3) 103 (2011) 847–878. []FGU2 J.F. Fernando, J.M. Gamboa, C. Ueno: Properties of the boundary of polynomial and regular images of Rn. Mathematical contributions in honor of Juan Tarres, 159–178, Univ. Complut.Madrid, Fac. Mat., adrid: 2012. []FU1 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 http://imrn.oxfordjournals.org/content/early/2013/06/17/imrn.rnt112.full .pdf?keytype=ref&ijkey=PiOgJzspWYsUzGp []FU2 J.F. Fernando, C. Ueno: On the complements of 3-dimensional convex polyhedra as polynomial images of R3. Internat. J. Math. XXX (2014, accepted), no. X, XXX-XXX. []G J.M. Gamboa: Reelle algebraische Geometrie, June,10th ´ 16th (1990), Oberwolfach. []Ha J. Harris: Algebraic Geometry. A first course. raduate Texts in Mathematics, 133. Springer-Verlag, New York: 1992. []H1 R. Hartshorne: Ample subvarieties of algebraic varieties. Notes written in collaboration with C. Musili. Lecture Notes in Mathematics, 156 Springer-Verlag, erlin-New York: 1970. []H2 R. Hartshorne: Algebraic geometry. Graduate Texts in Mathematics, 52 Springer-Verlag, New York-Heidelberg:1977. []J1 Z. Jelonek: Testing sets for properness of olynomial mappings. Math. Ann. 315 (1999), no. 1,1–35. []J2 Z. Jelonek: Geometry of real polynomial mappings. Math. Z., 239 (2002), no. 2, 321–333. []JK Z. Jelonek, K. Kurdyka: Reaching generalized critical values of a polynomial. Math. Z. (2014, to appear), no. X, XXX-XXX. arXiv:1203.0539v2.pdf []M D. Mumford: Algebraic geometry. I. Complex projective varieties. Grundlehren der Mathematis-chen issenschaften, 221. Springer-Verlag, Berlin-New York: 1976. []P S. Pinchuk: A counterexample to the real Jacobian Conjecture, Math. Z. 217 (1994), 1–4. []Sh1 I.R. Shafarevich: Basic Algebraic Geometry I. Varieties in projective space. Second edition. Trans-lated from the 1988 Russian edition and with notes by iles Reid. Springer-Verlag, Berlin: 1994. []Sh2 I.R. Shafarevich: Basic Algebraic Geometry II. Schemes and complex manifolds. Second edition. Translated from the 1988 Russian edition by Miles Reid. Springer-erlag, Berlin: 1994. []S E.H. Spanier: Algebraic topology. Springer-Verlag, New York-Berlin: 1981. []U1 C. Ueno: A note on boundaries of open polynomial images of R2. Rev. Mat. Iberoam. 24 (2008),981-988. []U2 C. Ueno: On convex polygons and their complements as images of regular and polynomial maps of R2. J. Pure Appl. Algebra 216 (2012), no. 11, 2436–2448. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 499732d5-c130-4ea6-8541-c4ec934da408 | |
| relation.isAuthorOfPublication.latestForDiscovery | 499732d5-c130-4ea6-8541-c4ec934da408 |
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