2005/06/12 by Bernd Sturmfels, Sturmfels, Bernd, Seth Sullivant +1 · 2 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications #math.AC #math.AG #math.CO
paper · pdf · doi:10.48550/arxiv.math/0506223
23 pages, 3 figures, The end of Section 5 has been rewritten
openalex publication_date 2005/06/12 · arxiv created 2005/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal of the secant ideal coincides with the secant ideal of the initial ideal. For toric varieties, this leads to the notion of delightful triangulations of convex polytopes.