Terracini拟阵：割线与嵌入并的代数拟阵
Terracini matroids: algebraic matroids of secants and embedded joins
AI总结：
本文受Terracini引理启发提出拟阵的Terracini并概念，研究代数拟阵在代数簇并与割线运算下的性质，明确并集代数拟阵与组成部分拟阵并的一致条件，并给出环面曲面与三维环面簇相关应用。
摘要：
代数几何的应用推动了近期代数拟阵领域的大量研究。代数拟阵可编码代数簇上坐标函数之间的代数依赖关系。本文研究了代数拟阵在代数簇的并与割线运算下的性质。受Terracini引理启发，我们提出了拟阵的Terracini并概念，用于刻画何时并集的代数拟阵与其各组成部分的代数拟阵的拟阵并相一致。我们还通过讨论其对环面曲面与三维环面簇的意义，阐释了研究结果的应用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
