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.
Rapagnetta, A., Sabatino, P. (2011). Surfaces with surjective endomorphisms of any given degree. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 60(3), 417-436 [10.1007/s12215-011-0068-9].
Surfaces with surjective endomorphisms of any given degree
RAPAGNETTA, ANTONIO;
2011-01-01
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.File | Dimensione | Formato | |
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