Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1209-1260 |
| Seitenumfang | 52 |
| Fachzeitschrift | Taiwanese journal of mathematics |
| Jahrgang | 29 |
| Ausgabenummer | 6 |
| Frühes Online-Datum | 4 Dez. 2024 |
| Publikationsstatus | Veröffentlicht - Dez. 2025 |
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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Taiwanese journal of mathematics, Jahrgang 29, Nr. 6, 12.2025, S. 1209-1260.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On the Cohomologically Trivial Automorphisms of Elliptic Surfaces I
T2 - χ(S) = 0
AU - Catanese, Fabrizio
AU - Frapporti, Davide
AU - Gleißner, Christian
AU - Liu, Wenfei
AU - Schütt, Matthias
N1 - Publisher Copyright: © 2025, Mathematical Society of the Rep. of China. All rights reserved.
PY - 2025/12
Y1 - 2025/12
N2 - 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.
AB - 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.
KW - algebraic surfaces
KW - automorphisms
KW - cohomologically trivial automorphisms
KW - compact Kähler manifolds
KW - Enriques–Kodaira classification
KW - topologically trivial automorphisms
UR - http://www.scopus.com/inward/record.url?scp=105027007058&partnerID=8YFLogxK
U2 - 10.11650/tjm/241106
DO - 10.11650/tjm/241106
M3 - Article
AN - SCOPUS:105027007058
VL - 29
SP - 1209
EP - 1260
JO - Taiwanese journal of mathematics
JF - Taiwanese journal of mathematics
SN - 1027-5487
IS - 6
ER -