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Pré-Publication, Document De Travail Année : 2021

MULTIGRADED SYLVESTER FORMS, DUALITY AND ELIMINATION MATRICES

Résumé

In this paper we study the equations of the elimination ideal associated with n + 1 generic multihomogeneous polynomials defined over a product of projective spaces of dimension n. We first prove a duality property and then make this duality explicit by introducing multigraded Sylvester forms. These results provide a partial generalization of similar properties that are known in the setting of homogeneous polynomial systems defined over a single projective space. As an important consequence, we derive a new family of elimination matrices that can be used for solving zero-dimensional multiprojective polynomial systems by means of linear algebra methods.
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Dates et versions

hal-03202525 , version 1 (07-10-2021)
hal-03202525 , version 2 (02-12-2022)

Identifiants

  • HAL Id : hal-03202525 , version 1

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Marc Chardin, Laurent Busé, Navid Nemati. MULTIGRADED SYLVESTER FORMS, DUALITY AND ELIMINATION MATRICES. 2021. ⟨hal-03202525v1⟩
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