2025/05/18 by Asano, Takumi · 1 citation
Mathematics · #14A10(Primary) #14E30(Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2505.12416
openalex publication_date 2025/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Miyanishi conjecture claims that for any variety over an algebraically closed field of characteristic zero, any endomorphism of such a variety which is injective outside a closed subset of codimension at least 2 is bijective. We prove Miyanishi conjecture for any quasi-projective variety X which is a dense open subset of a ℚ-factorial normal projective variety X such that codim (X ∖ X) ≥ 2 with the ample canonical divisor or the ample anti-canonical divisor. Also, we observe Miyanishi conjecture without the conditions of its canonical divisor by using minimal model program. In particular, we prove Miyanishi conjecture in the case that X has canonical singularities and X has the canonical model which is obtained by divisorial contractions.