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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Detalles Bibliográficos
Autores principales:	Botbol, N., Busé, L., Chardin, M., Hassanzadeh, S.H., Simis, A., Tran, Q.H.
Formato:	JOUR
Materias:	Bigraded base ideal Bigraded rational maps Birationality criteria Jacobian dual rank Rees algebras
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_07477171_v81_n_p69_Botbol
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_07477171_v81_n_p69_Botbol
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spelling	todo:paper_07477171_v81_n_p69_Botbol2023-10-03T15:39:01Z Effective criteria for bigraded birational maps Botbol, N. Busé, L. Chardin, M. Hassanzadeh, S.H. Simis, A. Tran, Q.H. 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 JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Botbol, N. Busé, L. Chardin, M. Hassanzadeh, S.H. Simis, A. Tran, Q.H. 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
format	JOUR
author	Botbol, N. Busé, L. Chardin, M. Hassanzadeh, S.H. Simis, A. Tran, Q.H.
author_facet	Botbol, N. Busé, L. Chardin, M. Hassanzadeh, S.H. Simis, A. Tran, Q.H.
author_sort	Botbol, N.
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
url	http://hdl.handle.net/20.500.12110/paper_07477171_v81_n_p69_Botbol
work_keys_str_mv	AT botboln effectivecriteriaforbigradedbirationalmaps AT busel effectivecriteriaforbigradedbirationalmaps AT chardinm effectivecriteriaforbigradedbirationalmaps AT hassanzadehsh effectivecriteriaforbigradedbirationalmaps AT simisa effectivecriteriaforbigradedbirationalmaps AT tranqh effectivecriteriaforbigradedbirationalmaps
_version_	1807324128832651264

Effective criteria for bigraded birational maps

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