Separation of semialgebraic sets
| dc.contributor.author | Acquistapace, Francesca | |
| dc.contributor.author | Andradas Heranz, Carlos | |
| dc.contributor.author | Broglia, Fabrizio | |
| dc.date.accessioned | 2023-06-20T16:49:42Z | |
| dc.date.available | 2023-06-20T16:49:42Z | |
| dc.date.issued | 1999 | |
| dc.description.abstract | We study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of spaces of orderings, named geometric, which suffice to test separation and that reduce the problem to the study of the behaviour of the semialgebraic sets in their boundary. Then we derive several characterizations for the generic separation, among which there is a geometric criterion that can be tested algorithmically. Finally we show how to check recursively whether we can pass from generic separation to separation, obtaining a decision procedure for solving the problem. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | EC | |
| dc.description.sponsorship | GNSAGA | |
| dc.description.sponsorship | CNR | |
| dc.description.sponsorship | MURST | |
| dc.description.sponsorship | DGICYT | |
| dc.description.sponsorship | Fundacion del Amo, UCM. | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14799 | |
| dc.identifier.doi | 10.1090/S0894-0347-99-00302-1 | |
| dc.identifier.issn | 0894-0347 | |
| dc.identifier.officialurl | http://www.ams.org/jourcgi/jrnl_toolbar_nav/jams_all | |
| dc.identifier.relatedurl | http://www.ams.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57156 | |
| dc.issue.number | 3 | |
| dc.journal.title | Journal of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 728 | |
| dc.page.initial | 703 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | CHRX-CT94-0506. | |
| dc.relation.projectID | PB95-0354 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | decidability of separation problem of semialgebraic sets | |
| dc.subject.keyword | algorithm | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | Separation of semialgebraic sets | |
| dc.type | journal article | |
| dc.volume.number | 12 | |
| dcterms.references | [AcAnBg] F. Acquistapace, C. Andradas, F. Broglia: \Classication of obstructions for separation of Semialgebraic Sets in dimension 3", Rev. Matematica U.C.M. 10 (numero suplementario) (1997) 27{49. CMP 98:05 [AcBgFo] F. Acquistapace, F. Broglia, E. Fortuna: \A separation theorem in dimension 3", Nagoya Math. Journal 143 (1996) 171{193. MR 97k:14056 [AnBrRz] C. Andradas, L. Br¨ocker, J.M. Ruiz: Constructible sets in real geometry, Ergeb. Math. 33, Springer-Verlag Berlin-Heidelberg-New York, 1996. MR 98e:14056 [AnRz1] C. Andradas, J.M. Ruiz: \More on basic semialgebraic sets", in Real Algebraic and analytic geometry, Lect. Notes in Math. 1524, Springer-Verlag, New York, (1992), 128-139. MR 94g:14030 [AnRz2] C. Andradas, J.M. Ruiz: \Low dimensional sections of basic semialgebraic sets", Illinois J. of Math. 38 (1994), 303-326. MR 95d:14056 [AnRz3] C. Andradas, J.M. Ruiz: \Ubiquity of Lojasiewicz example of a non-basic semialgebraic set", Michigan Math. J. 41 (1994). MR 96e:14064 [BeNe] E. Becker, R. Neuhaus: \Computation of real radicals of polynomial ideals", Proc. MEGA 92, Nice, France, Birkhauser (1993) 1{20. MR 94g:12001 [BiMi] E. Bierstone, P. Milman: \Canonical desingularization in characteristic zero by blowing-up the maximum strata of a local invariant", Inventiones Math. 128 (1997), 207-302. MR 98e:14010 [BCR] J. Bochnak, M. Coste, M.-F. Roy: Geometrie algebrique reelle, Ergeb. Math. 12, Springer-Verlag, Berlin-Heidelberg-New York, 1987. MR 90b:14030 [BoEf] J. Bochnak, G. Efroymson: \Real Algebraic geometry and the Hilbert 17th problem". Math. Ann. 251 (1980) 213{241. MR 81k:14023 [Br1] L. Br¨ocker: \Spaces of Orderings and semialgebraic sets", Canadian Math. Society conference proc. 4 (1984) 231{248. MR 86m:12002 [Br2] L. Br¨ocker: \Characterization of fans and hereditarily pythagorean elds", Math. Z. 151 (1976) 149{163. MR 54:10224 [Br3] L. Br¨ocker: \On the separation of basic semialgebraic sets by polynomials" Manuscripta Math. 60 (1988) 497{508 MR 89d:14034 [Br4] L. Br¨ocker: \On basic semialgebraic sets", Expo. Math. 9 (1991) 289-334. MR 93b:14085 [BrSt] L. Br¨ocker, G. Stengle: \On the Mostowski number", Math. Z. 203 (1990) 629{633. MR 91g:14058 [He] G. Hermann: \Die Frage der endlich vielen Schritte in der Theorie der Polynomideale", Math. Annalen 95 (1926). [Hk] H. Hironaka: \Resolution of singularities of an algebraic variety over a eld of characteristic zero", Annals of Math. 79 (1964) I:109-123, II:205-326. MR 33:7333 [Mo] T. Mostowski: \Some properties of the ring of Nash functions", Ann. Scuola Norm. Sup. Pisa 3 (1976) 245{266. MR 54:307 [Mr1] M. Marshall: \Classication of nite spaces of orderings", Canad. J. Math. 31 (1979) 320-330. MR 80i:10026 [Mr2] M. Marshall: \Quotients and inverse limits of spaces of orderings", Canad. J. Math. 31 (1979) 604-616. MR 80f:10021 [Mr3] M. Marshall: \The Witt ring of a space of orderings", Trans. Amer. Math. Soc. 258 (1980) 505-521. MR 81b:10012 [Mr4] M. Marshall: \Spaces of orderings IV", Canad. J. Math. 32 (1980) 603-627. MR 81m:10035 [Mr5] M. Marshall: \Spaces of orderings and Abstract Real Spectra", Lect. Notes in Math. 1636, Springer-Verlag, New York, (1997). MR 98b:14041 [Ne] R. Neuhaus: \Computation of real radicals of polynomial ideals II", Proc. MEGA 92, Nice, France, Birkhauser (1993). MR 94g:12001 [Pr] A. Prestel: \Model Theory for the Real Algebraic Geometer", to appear as a Quaderni del Dottorato del Dipartimento de Matematica, Universita di Pisa (1998). [Rz] J. Ruiz: \A note on a separation problem", Archiv der Mathematik 43 (1984) 422-426. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a74c23fe-4059-4e73-806b-71967e14ab67 | |
| relation.isAuthorOfPublication.latestForDiscovery | a74c23fe-4059-4e73-806b-71967e14ab67 |
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