## 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

#### Université Côte d'Azur, Inria, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak0c57ad7cb0a6812620b54fb8e91ee6a4').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy0c57ad7cb0a6812620b54fb8e91ee6a4 = 'l&#97;&#117;r&#101;nt.b&#117;s&#101;' + '&#64;'; addy0c57ad7cb0a6812620b54fb8e91ee6a4 = addy0c57ad7cb0a6812620b54fb8e91ee6a4 + '&#105;nr&#105;&#97;' + '&#46;' + 'fr'; var addy_text0c57ad7cb0a6812620b54fb8e91ee6a4 = 'l&#97;&#117;r&#101;nt.b&#117;s&#101;' + '&#64;' + '&#105;nr&#105;&#97;' + '&#46;' + 'fr';document.getElementById('cloak0c57ad7cb0a6812620b54fb8e91ee6a4').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy0c57ad7cb0a6812620b54fb8e91ee6a4 + '\'>'+addy_text0c57ad7cb0a6812620b54fb8e91ee6a4+'<\/a>';

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).