2021/04/07 by Hsueh-Yung Lin, Keiji Oguiso, Lin, Hsueh-Yung +3
Mathematics · #14J50 #16P90 #16S38 #32H50 #37B40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2104.03423
openalex publication_date 2021/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f be a zero entropy automorphism of a compact Kähler manifold X. We study the polynomial log-volume growth Plov(f) of f in light of the dynamical filtrations introduced in our previous work with T.-C. Dinh. We obtain new upper bounds and lower bounds of Plov(f). As a corollary, we completely determine Plov(f) when dim X = 3, extending a result of Artin--Van den Bergh for surfaces. When X is projective, Plov(f) + 1 coincides with the Gelfand--Kirillov dimensions GKdim(X,f) of the twisted homogeneous coordinate rings associated to (X,f). Reformulating these results for GKdim(X,f), we improve Keeler's bounds of GKdim(X,f) and provide effective upper bounds of GKdim(X,f) which only depend on dim X.