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arXiv · 2505.09204

The Segre Determinant

Elizabeth Pratt
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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.

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Elizabeth Pratt. 2025-10-07. The Segre Determinant. https://doi.org/10.2140/om.2026.3.127

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