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arXiv · 2511.03389

Terracini matroids: algebraic matroids of secants and embedded joins

Fatemeh Mohammadi·Jessica Sidman·Louis Theran
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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.

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Fatemeh Mohammadi, Jessica Sidman, Louis Theran. 2025-11-05. Terracini matroids: algebraic matroids of secants and embedded joins. https://arxiv.org/abs/2511.03389

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