The Segre Determinant
Algebraic Geometry
2026-05-20 v2
Abstract
The Segre determinant is a polynomial which encodes the condition for points to lie on a bilinear hypersurface in the product of projective spaces. We study Segre determinants and compute them in various coordinate systems. We show that the Segre determinant represents the Chow-Lam form of a generic torus orbit in the Grassmannian. These Chow-Lam forms were introduced as a generalization of Chow forms for projective varieties, and enjoy many similar properties. We also present applications to algebraic vision and to Chow quotients of Grassmannians.
Keywords
Cite
@article{arxiv.2505.09204,
title = {The Segre Determinant},
author = {Elizabeth Pratt},
journal= {arXiv preprint arXiv:2505.09204},
year = {2026}
}
Comments
16 pages, 2 figures