On the cohomologically trivial automorphisms of elliptic surfaces I: $χ(S)=0$

verfasst von

Fabrizio Catanese, Davide Frapporti, Christian Gleissner, Wenfei Liu, Matthias Schütt

Abstract

In this first part we describe the group AutZ(S) of cohomologically trivial automorphisms of a properly elliptic surface (a minimal surface S with Kodaira dimension κ(S)=1), in the initial case χ(OS)=0.
In particular, in the case where AutZ(S) is finite, we give the upper bound 4 for its cardinality, showing more precisely that if AutZ(S) is nontrivial, it is one of the following groups: Z/2,Z/3,(Z/2)^2. We also show with easy examples that the groups Z/2,Z/3 do effectively occur.
Respectively, in the case where AutZ(S) is infinite, we give the sharp upper bound 2 for the number of its connected components.

Organisationseinheit(en)

Institut für Algebraische Geometrie

Typ

Preprint

Publikationsdatum

29.08.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)