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Journal Articles Journal of Algebra Year : 2022

Multigraded Sylvester forms, Duality and Elimination Matrices

Abstract

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 and versions

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

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Laurent Busé, Marc Chardin, Navid Nemati. Multigraded Sylvester forms, Duality and Elimination Matrices. Journal of Algebra, 2022, 609 (1), pp.514-546. ⟨10.1016/j.jalgebra.2022.06.022⟩. ⟨hal-03202525v2⟩
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