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arXiv · 2104.08941

Multigraded Sylvester forms, Duality and Elimination Matrices

Laurent Busé·Marc Chardin·Navid Nemati
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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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Laurent Busé, Marc Chardin, Navid Nemati. 2021-04-18. Multigraded Sylvester forms, Duality and Elimination Matrices. https://arxiv.org/abs/2104.08941

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