On the Cohomologically Trivial Automorphisms of Elliptic Surfaces I: χ(S) = 0

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OriginalspracheEnglisch
Seiten (von - bis)1209-1260
Seitenumfang52
FachzeitschriftTaiwanese journal of mathematics
Jahrgang29
Ausgabenummer6
Frühes Online-Datum4 Dez. 2024
PublikationsstatusVeröffentlicht - 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.

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On the Cohomologically Trivial Automorphisms of Elliptic Surfaces I: χ(S) = 0. / Catanese, Fabrizio; Frapporti, Davide; Gleißner, Christian et al.
in: Taiwanese journal of mathematics, Jahrgang 29, Nr. 6, 12.2025, S. 1209-1260.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Catanese F, Frapporti D, Gleißner C, Liu W, Schütt M. On the Cohomologically Trivial Automorphisms of Elliptic Surfaces I: χ(S) = 0. Taiwanese journal of mathematics. 2025 Dez;29(6):1209-1260. Epub 2024 Dez 4. doi: 10.11650/tjm/241106
Catanese, Fabrizio ; Frapporti, Davide ; Gleißner, Christian et al. / On the Cohomologically Trivial Automorphisms of Elliptic Surfaces I : χ(S) = 0. in: Taiwanese journal of mathematics. 2025 ; Jahrgang 29, Nr. 6. S. 1209-1260.
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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

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KW - algebraic surfaces

KW - automorphisms

KW - cohomologically trivial automorphisms

KW - compact Kähler manifolds

KW - Enriques–Kodaira classification

KW - topologically trivial automorphisms

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