2015/11/24 by Roger Dellaca, Dellaca, Roger
Mathematics · #13A02 #13D40 #14C05 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1511.07859
openalex publication_date 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a form of the Gotzmann representation of the Hilbert polynomial based on rank and generating degrees of a module, which allow for a generalization of Gotzmann's Regularity Theorem. Under an additional assumption on the generating degrees, the Gotzmann regularity bound becomes sharp. An analoguous modification of the Macaulay representation is used along the way, which generalizes the theorems of Macaulay and Green, and Gotzmann's Persistence Theorem.