MULTIGRADED SYLVESTER FORMS, DUALITY AND ELIMINATION MATRICES

Marc Chardin (1, 2) , Laurent Busé (3) , Navid Nemati (3)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 CNRS - Centre National de la Recherche Scientifique
3 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

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.

Domaines: Algèbre commutative [math.AC]

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