2007/10/01 by Morgan Sherman, Sherman, Morgan · 2 citations
Mathematics · #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.0710.0186
openalex publication_date 2007/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gotzmann's Persistence states that the growth of an arbitrary ideal can be controlled by comparing it to the growth of the lexicographic ideal. This is used, for instance, in finding equations which cut out the Hilbert scheme (of subschemes of Pn with fixed Hilbert polynomial) sitting inside an appropriate Grassmannian. We introduce the notion of an \it extremal ideal which extends the notion of the lex ideal to other term orders. We then state and prove a version of Gotzmann's theorem for these ideals, valid in an open subset of a Grassmannian.