Terracini matroids: algebraic matroids of secants and embedded joins
Combinatorics
2026-05-15 v2 Symbolic Computation
Commutative Algebra
Algebraic Geometry
Abstract
Applications of algebraic geometry have sparked much recent work on algebraic matroids. An algebraic matroid encodes algebraic dependencies among coordinate functions on a variety. We study the behavior of algebraic matroids under joins and secants of varieties. Motivated by Terracini's lemma, we introduce the notion of a Terracini union of matroids, which captures when the algebraic matroid of a join coincides with the matroid union of the algebraic matroids of its summands. We illustrate applications of our results with a discussion of the implications for toric surfaces and threefolds.
Cite
@article{arxiv.2511.03389,
title = {Terracini matroids: algebraic matroids of secants and embedded joins},
author = {Fatemeh Mohammadi and Jessica Sidman and Louis Theran},
journal= {arXiv preprint arXiv:2511.03389},
year = {2026}
}