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：代数几何的应用近年来极大地推动了代数拟阵的研究。代数拟阵编码了簇上坐标函数之间的代数依赖关系。我们研究了簇的联与割线操作下代数拟阵的行为。受 Terracini 引理的启发，我们引入了拟阵的 Terracini 并的概念，该概念刻画了联的代数拟阵何时与其各分量代数拟阵的拟阵并相一致。我们通过讨论其对环面曲面与三维环面簇的影响，展示了我们结果的应用。