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dc.contributor.author
Dickenstein, Alicia Marcela
dc.contributor.author
Herrero, Maria Isabel
dc.contributor.author
Mourrain, Bernard
dc.date.available
2023-08-29T19:01:03Z
dc.date.issued
2022-12
dc.identifier.citation
Dickenstein, Alicia Marcela; Herrero, Maria Isabel; Mourrain, Bernard; Curve valuations and mixed volumes in the implicitization of rational varieties; Academic Press Inc Elsevier Science; Journal of Algebra; 612; 12-2022; 691-721
dc.identifier.issn
0021-8693
dc.identifier.uri
http://hdl.handle.net/11336/209832
dc.description.abstract
We address the description of the tropicalization of families of rational varieties under parametrizations with prescribed support, via curve valuations. We recover and extend results by Sturmfels, Tevelev and Yu for generic coefficients, considering rational parametrizations with non-trivial denominator. The advantage of our point of view is that it can be generalized to deal with non-generic parametrizations. We provide a detailed analysis of the degree of the closed image, based on combinatorial conditions on the relative positions of the supports of the polynomials defining the parametrization. We obtain a new formula and finer bounds on the degree, when the supports of the polynomials are different. We also present a new formula and bounds for the order at the origin in case the closed image is a hypersurface.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Academic Press Inc Elsevier Science
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
GENERALIZED PUISEUX SERIES
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IMPLICITIZATION
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NEWTON POLYTOPE
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TROPICAL GEOMETRY
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Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Curve valuations and mixed volumes in the implicitization of rational varieties
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-07-07T22:41:45Z
dc.journal.volume
612
dc.journal.pagination
691-721
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Dickenstein, Alicia Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.description.fil
Fil: Herrero, Maria Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.description.fil
Fil: Mourrain, Bernard. Université Côte d'Azur; Francia
dc.journal.title
Journal of Algebra
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869322004306
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1016/j.jalgebra.2022.08.026
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