Session S34 - Symbolic and Numerical Computation with Polynomials

Wednesday, July 21, 16:00 ~ 16:30 UTC-3

Multigraded Sylvester forms, duality and elimination matrices

Laurent Busé

Université Côte d'Azur, Inria, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, we will consider the equations of the elimination ideal associated to $n+1$ generic multihomogeneous polynomials defined over a product of projective spaces of dimension $n$. We will discuss a duality property and introduce multigraded Sylvester forms in order to make this latter duality explicit. 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, that we will also recall. We will also discuss a new family of elimination matrices that can be used for solving zero-dimensional multiprojective polynomial systems by means of linear algebra methods.

Joint work with Marc Chardin (Institut de Mathématiques de Jussieu, CNRS, Sorbonne Université) and Navid Nemati (Université Côte d'Azur, Inria).

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