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NO COHOMOLOGICALLY TRIVIAL NONTRIVIAL AUTOMORPHISM OF GENERALIZED KUMMER MANIFOLDS

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  05 November 2018

KEIJI OGUISO
KEIJI OGUISO*
Affiliation:
Mathematical Sciences, the University of Tokyo, Meguro Komaba 3-8-1, Tokyo, Japan email oguiso@ms.u-tokyo.ac.jp Korea Institute for Advanced Study, Hoegiro 87, Seoul, 133-722, Korea
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Abstract

For a hyper-Kähler manifold deformation equivalent to a generalized Kummer manifold, we prove that the action of the automorphism group on the total Betti cohomology group is faithful. This is a sort of generalization of a work of Beauville and a more recent work of Boissière, Nieper-Wisskirchen, and Sarti, concerning the action of the automorphism group of a generalized Kummer manifold on the second cohomology group.

MSC classification

Primary: 14J50: Automorphisms of surfaces and higher-dimensional varieties 14J40: $n$-folds ($n>4$)
Type
Article
Information
Nagoya Mathematical Journal , Volume 239 , September 2020 , pp. 110 - 122
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Copyright
© 2018 Foundation Nagoya Mathematical Journal

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Footnotes

The author is supported by JSPS Grant-in-Aid (S) No 25220701, JSPS Grant-in-Aid (S) 15H05738, JSPS Grant-in-Aid (B) 15H03611, and by KIAS Scholar Program.

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