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Minimal models of nilmanifolds


Author: Keizo Hasegawa
Journal: Proc. Amer. Math. Soc. 106 (1989), 65-71
MSC: Primary 32C10; Secondary 32M10, 53C15, 53C30, 53C55, 55P62
DOI: https://doi.org/10.1090/S0002-9939-1989-0946638-X
MathSciNet review: 946638
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Abstract: In this paper we first determine minimal models of nilmanifolds associated with given rational nilpotent Lie algebras. Then we study some properties of nilmanifolds through their associated Lie algebras and minimal models. In particular, we will see that a minimal model of a nilmanifold is formal if and only if it is a torus, and thus a non-toral nilmanifold has no complex structure which is birationally isomorphic to a Kähler manifold.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0946638-X
Keywords: Rational nilpotent Lie algebra, formality of minimal model, symplectic structure, Kähler structure
Article copyright: © Copyright 1989 American Mathematical Society

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