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arXiv · 1902.10386

Homotopy abelianity of the DG-Lie algebra controlling deformations of pairs (variety with trivial canonical bundle, line bundle)

Donatella Iacono·Marco Manetti
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Abstract

We investigate the deformations of pairs $(X,L)$, where $L$ is a line bundle on a smooth projective variety $X$, defined over an algebraically closed field $\mathbb{K}$ of characteristic 0. In particular, we prove that the DG-Lie algebra controlling the deformations of the pair $(X,L)$ is homotopy abelian whenever $X$ has trivial canonical bundle, and so these deformations are unobstructed.

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Donatella Iacono, Marco Manetti. 2019-02-27. Homotopy abelianity of the DG-Lie algebra controlling deformations of pairs (variety with trivial canonical bundle, line bundle). https://doi.org/10.1142/s0129167x21500865

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