Effective criteria for bigraded birational maps
In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that beca...
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2017
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v81_n_p69_Botbol http://hdl.handle.net/20.500.12110/paper_07477171_v81_n_p69_Botbol |
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paper:paper_07477171_v81_n_p69_Botbol2023-06-08T15:45:13Z Effective criteria for bigraded birational maps Bigraded base ideal Bigraded rational maps Birationality criteria Jacobian dual rank Rees algebras In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices. Then, we focus on rational maps from P1×P1 to P2 in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper. © 2016 Elsevier Ltd 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v81_n_p69_Botbol http://hdl.handle.net/20.500.12110/paper_07477171_v81_n_p69_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 |
Bigraded base ideal Bigraded rational maps Birationality criteria Jacobian dual rank Rees algebras |
| spellingShingle |
Bigraded base ideal Bigraded rational maps Birationality criteria Jacobian dual rank Rees algebras Effective criteria for bigraded birational maps |
| topic_facet |
Bigraded base ideal Bigraded rational maps Birationality criteria Jacobian dual rank Rees algebras |
| description |
In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices. Then, we focus on rational maps from P1×P1 to P2 in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper. © 2016 Elsevier Ltd |
| title |
Effective criteria for bigraded birational maps |
| title_short |
Effective criteria for bigraded birational maps |
| title_full |
Effective criteria for bigraded birational maps |
| title_fullStr |
Effective criteria for bigraded birational maps |
| title_full_unstemmed |
Effective criteria for bigraded birational maps |
| title_sort |
effective criteria for bigraded birational maps |
| publishDate |
2017 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v81_n_p69_Botbol http://hdl.handle.net/20.500.12110/paper_07477171_v81_n_p69_Botbol |
| _version_ |
1768543806463934464 |