2022/08/15 by A. Caminata, Caminata, Alessio, Yairon Cid‐Ruiz +3 · 3 citations
Mathematics · #05E40 #13H15 #13P10 #14C17 #52B40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2208.07238
openalex publication_date 2022/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study several properties of multihomogeneous prime ideals. We show that the multigraded generic initial ideal of a prime has very special properties, for instance, its radical is Cohen-Macaulay. We develop a comprehensive study of multidegrees in arbitrary positive multigraded settings. In these environments, we extend the notion of Cartwright-Sturmfels ideals by means of a standardization technique. Furthermore, we recover or extend important results in the literature, for instance: we provide a multidegree version of Hartshorne's result stating the upper semicontinuity of arithmetic degree under flat degenerations, and we give an alternative proof of Brion's result regarding multiplicity-free varieties.