Fitting ideals and multiple points of surface parameterizations

Given a birational parameterization ϕ of an algebraic surface S⊂P3, the purpose of this paper is to investigate the sets of points on S whose pre-image consists of k or more points, counting multiplicities. These points are described explicitly in terms of Fitting ideals of some graded parts of the...

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Detalles Bibliográficos
Autores principales: Botbol, N., Busé, L., Chardin, M.
Formato: JOUR
Materias:
Fibers of morphisms
Fitting ideals
Matrix representation
Rational maps
Symmetric and rees algebras
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00218693_v420_n_p486_Botbol
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00218693_v420_n_p486_Botbol
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spelling todo:paper_00218693_v420_n_p486_Botbol2023-10-03T14:21:32Z Fitting ideals and multiple points of surface parameterizations Botbol, N. Busé, L. Chardin, M. Fibers of morphisms Fitting ideals Matrix representation Rational maps Symmetric and rees algebras Given a birational parameterization ϕ of an algebraic surface S⊂P3, the purpose of this paper is to investigate the sets of points on S whose pre-image consists of k or more points, counting multiplicities. These points are described explicitly in terms of Fitting ideals of some graded parts of the symmetric algebra associated with the parameterization ϕ. To obtain this description, we show that the degree and dimension of a fiber could be computed by comparing the drop of rank of two explicit (representation) matrices associated with ϕ. © 2014. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00218693_v420_n_p486_Botbol
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fibers of morphisms
Fitting ideals
Matrix representation
Rational maps
Symmetric and rees algebras
spellingShingle Fibers of morphisms
Fitting ideals
Matrix representation
Rational maps
Symmetric and rees algebras
Botbol, N.
Busé, L.
Chardin, M.
Fitting ideals and multiple points of surface parameterizations
topic_facet Fibers of morphisms
Fitting ideals
Matrix representation
Rational maps
Symmetric and rees algebras
description Given a birational parameterization ϕ of an algebraic surface S⊂P3, the purpose of this paper is to investigate the sets of points on S whose pre-image consists of k or more points, counting multiplicities. These points are described explicitly in terms of Fitting ideals of some graded parts of the symmetric algebra associated with the parameterization ϕ. To obtain this description, we show that the degree and dimension of a fiber could be computed by comparing the drop of rank of two explicit (representation) matrices associated with ϕ. © 2014.
format JOUR
author Botbol, N.
Busé, L.
Chardin, M.
author_facet Botbol, N.
Busé, L.
Chardin, M.
author_sort Botbol, N.
title Fitting ideals and multiple points of surface parameterizations
title_short Fitting ideals and multiple points of surface parameterizations
title_full Fitting ideals and multiple points of surface parameterizations
title_fullStr Fitting ideals and multiple points of surface parameterizations
title_full_unstemmed Fitting ideals and multiple points of surface parameterizations
title_sort fitting ideals and multiple points of surface parameterizations
url http://hdl.handle.net/20.500.12110/paper_00218693_v420_n_p486_Botbol
work_keys_str_mv AT botboln fittingidealsandmultiplepointsofsurfaceparameterizations
AT busel fittingidealsandmultiplepointsofsurfaceparameterizations
AT chardinm fittingidealsandmultiplepointsofsurfaceparameterizations
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