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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2014
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v420_n_p486_Botbol http://hdl.handle.net/20.500.12110/paper_00218693_v420_n_p486_Botbol |
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paper:paper_00218693_v420_n_p486_Botbol2023-06-08T14:42:27Z Fitting ideals and multiple points of surface parameterizations 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v420_n_p486_Botbol 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 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. |
| 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 |
| publishDate |
2014 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v420_n_p486_Botbol http://hdl.handle.net/20.500.12110/paper_00218693_v420_n_p486_Botbol |
| _version_ |
1768545172592787456 |