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arXiv · 1011.5984

Surfaces with nontrivial surjective endomorphisms of any given degree

Antonio Rapagnetta·Pietro Sabatino
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Abstract

We present a complete classification of complex projective surfaces $X$ with nontrivial self-maps (i.e. surjective morphisms $f:X\rightarrow X$ 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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Antonio Rapagnetta, Pietro Sabatino. 2010-11-27. Surfaces with nontrivial surjective endomorphisms of any given degree. https://arxiv.org/abs/1011.5984

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