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Holomorphic Deformations of Balanced Cal...
Popovici, Dan...

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Holomorphic Deformations of Balanced Calabi-Yau $\partial\bar\partial$-Manifolds by Popovici, Dan ( Author )
Lemonjar Open Access
Australian National University
26-07-2023
Given a compact complex $n$-fold $X$ satisfying the $\partial\bar\partial$-lemma and supposed to have a trivial canonical bundle $K_X$ and to admit a balanced (=semi-K\"ahler) Hermitian metric $\omega$, we introduce the concept of deformations of $X$ that are {\bf co-polarised} by the balanced class $[\omega^{n-1}]\in H^{n-1,\,n-1}(X,\,\C)\subset H^{2n-2}(X,\,\C)$ and show that the resulting theory of balanced co-polarised deformations is a natural extension of the classical theory of K\"ahler polarised deformations in the context of Calabi-Yau or even holomorphic symplectic compact complex manifolds. The concept of Weil-Petersson metric still makes sense in this strictly more general, possibly non-K\"ahler context, while the Local Torelli Theorem still holds.
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Article
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English
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MYR 0.01
1
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http://arxiv.org/abs/1304.0331
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