## View abstract

### 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

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.