2025/11/05 by Fatemeh Mohammadi, Jessica Sidman, Mohammadi, Fatemeh +3
Computer Science · Mathematics · #05B35 #14N05 #14N07 #14Q15 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2511.03389
openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/08/01
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.