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.

翻译：代数几何的应用极大地推动了近期关于代数拟阵的研究。一个代数拟阵编码了簇上坐标函数间的代数依赖关系。本文研究簇的并与割线下代数拟阵的行为。受Terracini引理的启发，我们引入拟阵的Terracini并概念，该概念刻画了并的代数拟阵与其加项代数拟阵的拟阵并何时一致。通过讨论对环面曲面及三维流形的推论，我们展示了所获结果的应用。