2012/12/26 by Steven Dale Cutkosky, Cutkosky, Steven Dale · 4 citations
Mathematics · Medicine · #13D40 #14C40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Magnolia and Illicium research #Meromorphic and Entire Functions #math.AC #math.AG #msc:13D40 #msc:14C40
paper · pdf · doi:10.48550/arxiv.1212.6186
20 pages
arxiv created 2012/12/26 · openalex publication_date 2012/12/26 · arxiv updated 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Okounkov, Lazarsfeld and Mustata, and Kaveh and Khovanskii have shown that the growth of a graded linear series on a projective variety over an algebraically closed field is asymptotic to a polynomial. We give a complete description of the possible asymptotic growth of graded linear series on projective schemes over a perfect field. If the scheme is reduced, then the growth is polynomial like, but the growth can be very complex on nonreduced schemes. We also give an example of a graded family of m-primary ideals In in a nonreduced d-dimensional local ring R, such that the length of R/In divided by nd does not have a limit, even when restricted to any arithmetic sequence.