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Multigraded Sylvester forms, Duality and Elimination Matrices

Laurent Busé 1 Marc Chardin 2 Navid Nemati 1
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
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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Submitted on : Tuesday, April 20, 2021 - 8:12:55 AM
Last modification on : Thursday, April 7, 2022 - 1:58:25 PM

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  • HAL Id : hal-03202525, version 1
  • ARXIV : 2104.08941


Laurent Busé, Marc Chardin, Navid Nemati. Multigraded Sylvester forms, Duality and Elimination Matrices. 2021. ⟨hal-03202525⟩



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