Surfaces with nontrivial surjective endomorphisms of any given degree

2010/11/27 by Antonio Rapagnetta, Rapagnetta, Antonio, Pietro Sabatino +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1011.5984

Abstract

We present a complete classification of complex projective surfaces X with nontrivial self-maps (i.e. surjective morphisms f:X→ X which are not isomorphisms) of any given degree. The starting point of our classification are results contained in Fujimoto and Nakayama that provide a list of surfaces that admit at least one nontrivial self-map. We then proceed by a case by case analysis that blends geometrical and arithmetical arguments in order to exclude that certain prime numbers appear as degrees of nontrivial self-maps of certain surfaces.

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