Heights of varieties in multiprojective spaces and arithmetic nullstellensätze

We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of project...

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Detalles Bibliográficos
Autores principales: Krick, Teresa Elena Genoveva, Sombra, Martín
Publicado: 2013
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00129593_v46_n4_p549_Doandrea
http://hdl.handle.net/20.500.12110/paper_00129593_v46_n4_p549_Doandrea
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00129593_v46_n4_p549_Doandrea
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spelling paper:paper_00129593_v46_n4_p549_Doandrea2023-06-08T14:35:36Z Heights of varieties in multiprojective spaces and arithmetic nullstellensätze Krick, Teresa Elena Genoveva Sombra, Martín We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study this notion from the point of view of resultant theory and establish some of its basic properties, including its behavior with respect to intersections, projections and products. We obtain analogous results for the function field case, including a parametric Nullstellensatz. © 2013 Sociét. Mathématique de France. Tous droits réservé s. Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Sombra, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00129593_v46_n4_p549_Doandrea http://hdl.handle.net/20.500.12110/paper_00129593_v46_n4_p549_Doandrea
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study this notion from the point of view of resultant theory and establish some of its basic properties, including its behavior with respect to intersections, projections and products. We obtain analogous results for the function field case, including a parametric Nullstellensatz. © 2013 Sociét. Mathématique de France. Tous droits réservé s.
author Krick, Teresa Elena Genoveva
Sombra, Martín
spellingShingle Krick, Teresa Elena Genoveva
Sombra, Martín
Heights of varieties in multiprojective spaces and arithmetic nullstellensätze
author_facet Krick, Teresa Elena Genoveva
Sombra, Martín
author_sort Krick, Teresa Elena Genoveva
title Heights of varieties in multiprojective spaces and arithmetic nullstellensätze
title_short Heights of varieties in multiprojective spaces and arithmetic nullstellensätze
title_full Heights of varieties in multiprojective spaces and arithmetic nullstellensätze
title_fullStr Heights of varieties in multiprojective spaces and arithmetic nullstellensätze
title_full_unstemmed Heights of varieties in multiprojective spaces and arithmetic nullstellensätze
title_sort heights of varieties in multiprojective spaces and arithmetic nullstellensätze
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00129593_v46_n4_p549_Doandrea
http://hdl.handle.net/20.500.12110/paper_00129593_v46_n4_p549_Doandrea
work_keys_str_mv AT krickteresaelenagenoveva heightsofvarietiesinmultiprojectivespacesandarithmeticnullstellensatze
AT sombramartin heightsofvarietiesinmultiprojectivespacesandarithmeticnullstellensatze
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