2016/09/04 by Ekaterina Amerik, Alexandra Kuznetsova, Amerik, Ekaterina +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1609.00910
openalex publication_date 2016/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let B be a simply-connected projective variety such that the first cohomology groups of all line bundles on B are zero. Let E be a vector bundle over B and X=\mathbb P (E). It is easily seen that a power of any endomorphism of X takes fibers to fibers. We prove that if X admits an endomorphism which is of degree greater than one on the fibers then E splits into a direct sum of line bundles.