Mixed discriminants

The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise...

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Detalles Bibliográficos
Autores principales: Cattani, Eduardo H.C., Dickenstein, Alicia Marcela
Publicado: 2013
Materias:
A-discriminant
Cayley polytope
Degree
Matroid strata
Mixed Grassmannian
Multiple root
Tropical discriminant
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255874_v274_n3-4_p761_Cattani
http://hdl.handle.net/20.500.12110/paper_00255874_v274_n3-4_p761_Cattani
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00255874_v274_n3-4_p761_Cattani
record_format dspace
spelling paper:paper_00255874_v274_n3-4_p761_Cattani2023-06-08T14:53:24Z Mixed discriminants Cattani, Eduardo H.C. Dickenstein, Alicia Marcela A-discriminant Cayley polytope Degree Matroid strata Mixed Grassmannian Multiple root Tropical discriminant The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plücker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves. © 2012 Springer-Verlag Berlin Heidelberg. Fil:Cattani, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255874_v274_n3-4_p761_Cattani http://hdl.handle.net/20.500.12110/paper_00255874_v274_n3-4_p761_Cattani
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A-discriminant
Cayley polytope
Degree
Matroid strata
Mixed Grassmannian
Multiple root
Tropical discriminant
spellingShingle A-discriminant
Cayley polytope
Degree
Matroid strata
Mixed Grassmannian
Multiple root
Tropical discriminant
Cattani, Eduardo H.C.
Dickenstein, Alicia Marcela
Mixed discriminants
topic_facet A-discriminant
Cayley polytope
Degree
Matroid strata
Mixed Grassmannian
Multiple root
Tropical discriminant
description The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plücker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves. © 2012 Springer-Verlag Berlin Heidelberg.
author Cattani, Eduardo H.C.
Dickenstein, Alicia Marcela
author_facet Cattani, Eduardo H.C.
Dickenstein, Alicia Marcela
author_sort Cattani, Eduardo H.C.
title Mixed discriminants
title_short Mixed discriminants
title_full Mixed discriminants
title_fullStr Mixed discriminants
title_full_unstemmed Mixed discriminants
title_sort mixed discriminants
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255874_v274_n3-4_p761_Cattani
http://hdl.handle.net/20.500.12110/paper_00255874_v274_n3-4_p761_Cattani
work_keys_str_mv AT cattanieduardohc mixeddiscriminants
AT dickensteinaliciamarcela mixeddiscriminants
_version_ 1768545590234316800

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