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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Varieties with $ \mathbb{P}$-units


Author: Andreas Krug
Journal: Trans. Amer. Math. Soc. 370 (2018), 7959-7983
MSC (2010): Primary 14J32; Secondary 14J50, 14F05
DOI: https://doi.org/10.1090/tran/7218
Published electronically: May 30, 2018
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Abstract: We study the class of compact Kähler manifolds with trivial canonical bundle and the property that the cohomology of the trivial line bundle is generated by one element. If the square of the generator is zero, we get the class of strict Calabi-Yau manifolds. If the generator is of degree $ 2$, we get the class of compact hyperkähler manifolds. We provide some examples and structure results for the cases where the generator is of higher nilpotency index and degree. In particular, we show that varieties of this type are closely related to higher-dimensional Enriques varieties.


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Andreas Krug
Affiliation: Universität Marburg, Fachbereich 12 Mathematik und Informatik, Hans-Meerwein-Strasse 6, 35032 Marburg, Germany
Email: andkrug@outlook.de

DOI: https://doi.org/10.1090/tran/7218
Received by editor(s): July 27, 2016
Received by editor(s) in revised form: February 3, 2017, and February 21, 2017
Published electronically: May 30, 2018
Additional Notes: The early stages of this work were done while the author was financially supported by the research grant KR 4541/1-1 of the DFG (German Research Foundation).
Article copyright: © Copyright 2018 American Mathematical Society

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