2019/05/31 by Guolei Zhong · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Combinatorics #Discrete mathematics #Endomorphism #Gravitational singularity #Invariant (physics) #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Prime (order theory) #Projective variety #Pure mathematics #Surjective function #Upper and lower bounds #math.AG #msc:08A35 #msc:14E30 #msc:32H50
paper · pdf · doi:10.1007/s12220-020-00366-6
published as J. Geom. Anal. Vol. 31 (2021), no. 3, 2568-2593 · Changes in the structure; The Journal of Geometric Analysis (to appear)
openalex created_date 2019/05/29 · openalex publication_date 2020/02/12 · arxiv created 2020/02/14 · arxiv updated 2022/03/21 · openalex updated_date 2026/08/05
We consider an arbitrary int-amplified surjective endomorphism f of a normal projective variety X over ℂ and its f-1-stable prime divisors. We extend the early result for the case of polarized endomorphisms to the case of int-amplified endomorphisms. Assume further that X has at worst Kawamata log terminal singularities. We prove that the total number of f-1-stable prime divisors has an optimal upper bound dim X+ρ(X), where ρ(X) is the Picard number. Also, we give a sufficient condition for X to be rationally connected and simply connected. Finally, by running the minimal model program (MMP), we prove that, under some extra conditions, the end product of the MMP can only be an elliptic curve or a single point.