Details
| Originalsprache | Englisch |
|---|---|
| Publikationsstatus | Elektronisch veröffentlicht (E-Pub) - 29 Aug. 2024 |
Abstract
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.
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2024.
Publikation: Arbeitspapier/Preprint › Preprint
}
TY - UNPB
T1 - On the cohomologically trivial automorphisms of elliptic surfaces I: $χ(S)=0$
AU - Catanese, Fabrizio
AU - Frapporti, Davide
AU - Gleissner, Christian
AU - Liu, Wenfei
AU - Schütt, Matthias
N1 - 49 pages, to appear in a volume of the Taiwanese Journal of Mathematics dedicated to Yurii (Gennadievich) Prokhorov on the occasion of his 60th birthday
PY - 2024/8/29
Y1 - 2024/8/29
N2 - In this first part we describe the group $Aut_{\mathbb{Z}}(S)$ of cohomologically trivial automorphisms of a properly elliptic surface (a minimal surface $S$ with Kodaira dimension $\kappa(S)=1$), in the initial case $ \chi(\mathcal{O}_S) =0$. In particular, in the case where $Aut_{\mathbb{Z}}(S)$ is finite, we give the upper bound 4 for its cardinality, showing more precisely that if $Aut_{\mathbb{Z}}(S)$ is nontrivial, it is one of the following groups: $\mathbb{Z}/2, \mathbb{Z}/3, (\mathbb{Z}/2)^2$. We also show with easy examples that the groups $\mathbb{Z}/2, \mathbb{Z}/3$ do effectively occur. Respectively, in the case where $Aut_{\mathbb{Z}}(S)$ is infinite, we give the sharp upper bound 2 for the number of its connected components.
AB - In this first part we describe the group $Aut_{\mathbb{Z}}(S)$ of cohomologically trivial automorphisms of a properly elliptic surface (a minimal surface $S$ with Kodaira dimension $\kappa(S)=1$), in the initial case $ \chi(\mathcal{O}_S) =0$. In particular, in the case where $Aut_{\mathbb{Z}}(S)$ is finite, we give the upper bound 4 for its cardinality, showing more precisely that if $Aut_{\mathbb{Z}}(S)$ is nontrivial, it is one of the following groups: $\mathbb{Z}/2, \mathbb{Z}/3, (\mathbb{Z}/2)^2$. We also show with easy examples that the groups $\mathbb{Z}/2, \mathbb{Z}/3$ do effectively occur. Respectively, in the case where $Aut_{\mathbb{Z}}(S)$ is infinite, we give the sharp upper bound 2 for the number of its connected components.
KW - math.AG
KW - math.CV
KW - 14J50, 14J80, 14J27, 14H30, 14F99, 32L05, 32M99, 32Q15, 32Q55
M3 - Preprint
BT - On the cohomologically trivial automorphisms of elliptic surfaces I: $χ(S)=0$
ER -