Explicit estimates for polynomial systems defining irreducible smooth complete intersections
- Autores
- Von zur Gathen, Joachim; Matera, Guillermo
- Año de publicación
- 2019
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- This paper deals with properties of the algebraic variety defined as the set of zeros of a “typical” sequence of polynomials. We consider various types of “nice” varieties: set-theoretic and ideal-theoretic complete intersections, absolutely irreducible ones, and nonsingular ones. For these types, we present a nonzero “genericity” polynomial of explicitly bounded degree in the coefficients of the sequence that vanishes if its variety is not of the type. Here, the number of polynomials and their degrees are fixed. Over finite fields, this yields bounds on the number of such sequences. We also show that most sequences (of at least two polynomials) define a degenerate variety, namely an absolutely irreducible nonsingular hypersurface in some linear projective subspace.
Fil: Von zur Gathen, Joachim. Universitat Bonn; Alemania
Fil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina - Materia
-
ABSOLUTE IRREDUCIBILITY
COMPLETE INTERSECTIONS
FINITE FIELDS
NONSINGULARITY
POLYNOMIAL SYSTEMS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/149729
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Explicit estimates for polynomial systems defining irreducible smooth complete intersectionsVon zur Gathen, JoachimMatera, GuillermoABSOLUTE IRREDUCIBILITYCOMPLETE INTERSECTIONSFINITE FIELDSNONSINGULARITYPOLYNOMIAL SYSTEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper deals with properties of the algebraic variety defined as the set of zeros of a “typical” sequence of polynomials. We consider various types of “nice” varieties: set-theoretic and ideal-theoretic complete intersections, absolutely irreducible ones, and nonsingular ones. For these types, we present a nonzero “genericity” polynomial of explicitly bounded degree in the coefficients of the sequence that vanishes if its variety is not of the type. Here, the number of polynomials and their degrees are fixed. Over finite fields, this yields bounds on the number of such sequences. We also show that most sequences (of at least two polynomials) define a degenerate variety, namely an absolutely irreducible nonsingular hypersurface in some linear projective subspace.Fil: Von zur Gathen, Joachim. Universitat Bonn; AlemaniaFil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaPolish Academy of Sciences. Institute of Mathematics2019-03-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/149729Von zur Gathen, Joachim; Matera, Guillermo; Explicit estimates for polynomial systems defining irreducible smooth complete intersections; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 188; 3; 8-3-2019; 209-2400065-10361730-6264CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/188/3/112910/explicit-estimates-for-polynomial-systems-defining-irreducible-smooth-complete-intersectionsinfo:eu-repo/semantics/altIdentifier/doi/10.4064/aa8387-8-2018info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1512.05598info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:38:17Zoai:ri.conicet.gov.ar:11336/149729instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:38:18.025CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Explicit estimates for polynomial systems defining irreducible smooth complete intersections |
title |
Explicit estimates for polynomial systems defining irreducible smooth complete intersections |
spellingShingle |
Explicit estimates for polynomial systems defining irreducible smooth complete intersections Von zur Gathen, Joachim ABSOLUTE IRREDUCIBILITY COMPLETE INTERSECTIONS FINITE FIELDS NONSINGULARITY POLYNOMIAL SYSTEMS |
title_short |
Explicit estimates for polynomial systems defining irreducible smooth complete intersections |
title_full |
Explicit estimates for polynomial systems defining irreducible smooth complete intersections |
title_fullStr |
Explicit estimates for polynomial systems defining irreducible smooth complete intersections |
title_full_unstemmed |
Explicit estimates for polynomial systems defining irreducible smooth complete intersections |
title_sort |
Explicit estimates for polynomial systems defining irreducible smooth complete intersections |
dc.creator.none.fl_str_mv |
Von zur Gathen, Joachim Matera, Guillermo |
author |
Von zur Gathen, Joachim |
author_facet |
Von zur Gathen, Joachim Matera, Guillermo |
author_role |
author |
author2 |
Matera, Guillermo |
author2_role |
author |
dc.subject.none.fl_str_mv |
ABSOLUTE IRREDUCIBILITY COMPLETE INTERSECTIONS FINITE FIELDS NONSINGULARITY POLYNOMIAL SYSTEMS |
topic |
ABSOLUTE IRREDUCIBILITY COMPLETE INTERSECTIONS FINITE FIELDS NONSINGULARITY POLYNOMIAL SYSTEMS |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
This paper deals with properties of the algebraic variety defined as the set of zeros of a “typical” sequence of polynomials. We consider various types of “nice” varieties: set-theoretic and ideal-theoretic complete intersections, absolutely irreducible ones, and nonsingular ones. For these types, we present a nonzero “genericity” polynomial of explicitly bounded degree in the coefficients of the sequence that vanishes if its variety is not of the type. Here, the number of polynomials and their degrees are fixed. Over finite fields, this yields bounds on the number of such sequences. We also show that most sequences (of at least two polynomials) define a degenerate variety, namely an absolutely irreducible nonsingular hypersurface in some linear projective subspace. Fil: Von zur Gathen, Joachim. Universitat Bonn; Alemania Fil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina |
description |
This paper deals with properties of the algebraic variety defined as the set of zeros of a “typical” sequence of polynomials. We consider various types of “nice” varieties: set-theoretic and ideal-theoretic complete intersections, absolutely irreducible ones, and nonsingular ones. For these types, we present a nonzero “genericity” polynomial of explicitly bounded degree in the coefficients of the sequence that vanishes if its variety is not of the type. Here, the number of polynomials and their degrees are fixed. Over finite fields, this yields bounds on the number of such sequences. We also show that most sequences (of at least two polynomials) define a degenerate variety, namely an absolutely irreducible nonsingular hypersurface in some linear projective subspace. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-03-08 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/149729 Von zur Gathen, Joachim; Matera, Guillermo; Explicit estimates for polynomial systems defining irreducible smooth complete intersections; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 188; 3; 8-3-2019; 209-240 0065-1036 1730-6264 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/149729 |
identifier_str_mv |
Von zur Gathen, Joachim; Matera, Guillermo; Explicit estimates for polynomial systems defining irreducible smooth complete intersections; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 188; 3; 8-3-2019; 209-240 0065-1036 1730-6264 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/188/3/112910/explicit-estimates-for-polynomial-systems-defining-irreducible-smooth-complete-intersections info:eu-repo/semantics/altIdentifier/doi/10.4064/aa8387-8-2018 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1512.05598 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Polish Academy of Sciences. Institute of Mathematics |
publisher.none.fl_str_mv |
Polish Academy of Sciences. Institute of Mathematics |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.070432 |