The Vandermonde determinant identity in higher dimension

Itaï Ben Yaacov (1)

1 ICJ - Institut Camille Jordan

We generalise the Vandermonde determinant identity to one which tests whether a family of hypersurfaces in $\bP^n$ has an unexpected intersection point. The intended application is an asymptotic estimate of the volume of certain spaces of homogeneous polynomials on an embedded projective variety.

Mots clés: Vandermonde; determinant; hypersurface; intersection; resultant; Chow form

Domaines: Algèbre commutative [math.AC]

Itaï Ben Yaacov. The Vandermonde determinant identity in higher dimension. 2017. ⟨hal-00983858v3⟩