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

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.

5 pages; v2: title changed, major revision

References in corpus (3)

• Lectures on deformations of complex manifolds
• On deformations of pairs (manifold, coherent sheaf)
• Infinitesimal deformations of Hitchin pairs and Hitchin map