On the Classification of Quasihomogeneous Functions

We give a criterion for the existence of a non-degenerate quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation of this criterion to the necessary condition derived from the formula for the Poincar\'e polynomial. W...

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Detalles Bibliográficos
Autores principales: Kreuzer, Maximilian, Skarke, Harald
Lenguaje:eng
Publicado: 1992
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/BF02096569
http://cds.cern.ch/record/232877
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author Kreuzer, Maximilian
Skarke, Harald
author_facet Kreuzer, Maximilian
Skarke, Harald
author_sort Kreuzer, Maximilian
collection CERN
description We give a criterion for the existence of a non-degenerate quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation of this criterion to the necessary condition derived from the formula for the Poincar\'e polynomial. We further prove finiteness of the number of configurations for a given value of the singularity index. For the value 3 of this index, which is of particular interest in string theory, a constructive version of this proof implies an algorithm for the calculation of all non-degenerate configurations.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1992
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spelling cern-2328772020-07-23T02:44:57Zdoi:10.1007/BF02096569http://cds.cern.ch/record/232877engKreuzer, MaximilianSkarke, HaraldOn the Classification of Quasihomogeneous FunctionsMathematical Physics and MathematicsWe give a criterion for the existence of a non-degenerate quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation of this criterion to the necessary condition derived from the formula for the Poincar\'e polynomial. We further prove finiteness of the number of configurations for a given value of the singularity index. For the value 3 of this index, which is of particular interest in string theory, a constructive version of this proof implies an algorithm for the calculation of all non-degenerate configurations.We give a criterion for the existence of a non-degenerate quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation of this criterion to the necessary condition derived from the formula for the Poincar\'e polynomial. We further prove finiteness of the number of configurations for a given value of the singularity index. For the value 3 of this index, which is of particular interest in string theory, a constructive version of this proof implies an algorithm for the calculation of all non-degenerate configurations.CERN-TH-6373-92TUW-92-1hep-th/9202039CERN-TH-6373-92TUW-92-1oai:cds.cern.ch:2328771992
spellingShingle Mathematical Physics and Mathematics
Kreuzer, Maximilian
Skarke, Harald
On the Classification of Quasihomogeneous Functions
title On the Classification of Quasihomogeneous Functions
title_full On the Classification of Quasihomogeneous Functions
title_fullStr On the Classification of Quasihomogeneous Functions
title_full_unstemmed On the Classification of Quasihomogeneous Functions
title_short On the Classification of Quasihomogeneous Functions
title_sort on the classification of quasihomogeneous functions
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/BF02096569
http://cds.cern.ch/record/232877
work_keys_str_mv AT kreuzermaximilian ontheclassificationofquasihomogeneousfunctions
AT skarkeharald ontheclassificationofquasihomogeneousfunctions

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