2019/10/31 by Guolei Zhong · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Combinatorics #Dimension (graph theory) #Divisor (algebraic geometry) #Endomorphism #Fano plane #Geometry #Geometry and complex manifolds #Gravitational singularity #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Projective variety #Pure mathematics #Surjective function #Torus #math.AG #math.DS #msc:08A35 #msc:11G10 #msc:14E30
paper · pdf · open access · doi:10.4310/ajm.2021.v25.n3.a3
published in Asian Journal of Mathematics 25(3), 369-392 · Changes in the structure; Asian Journal of Mathematics (to appear)
openalex publication_date 2021/01/01 · arxiv created 2022/03/14 · arxiv updated 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let X be a normal compact Kähler space of dimension n. A surjective endomorphism f of such X is int-amplified if f^*ξ-ξ=η for some Kähler classes ξ and η. First, we show that this definition generalizes the notion in the projective setting. Second, we prove that for the cases of X being smooth, a surface or a threefold with mild singularities, if X admits an int-amplified endomorphism with pseudo-effective canonical divisor, then it is a Q-torus. Finally, we consider a normal compact Kähler threefold Y with only terminal singularities and show that, replacing f by a positive power, we can run the minimal model program (MMP) f-equivariantly for such Y and reach either a Q-torus or a Fano (projective) variety of Picard number one.