The Vandermonde determinant identity in higher dimension

TL;DR

This paper extends the Vandermonde determinant identity to higher dimensions, providing a new criterion for detecting unexpected intersection points among hypersurfaces in projective space.

Contribution

It introduces a generalized Vandermonde determinant identity applicable to higher-dimensional hypersurfaces, advancing intersection theory in algebraic geometry.

Findings

Derived a higher-dimensional Vandermonde determinant identity

Provided a new test for unexpected hypersurface intersections

Enhanced understanding of intersection behavior in projective spaces

Abstract

We generalise the Vandermonde determinant identity to one which tests whether a family of hypersurfaces in $\mathbf{P}^n$ has an unexpected intersection point.