2021/04/18 by Busé, Laurent, Chardin, Marc, Nemati, Navid · 1 citation
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)
paper · doi:10.48550/arxiv.2104.08941
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.