On deformations of pairs (manifold, coherent sheaf)

Abstract

We analyse infinitesimal deformations of pairs $(X,\mathcal{F})$ with $\mathcal{F}$ a coherent sheaf on a smooth projective manifold $X$ over an algebraic closed field of characteristic $0$. We describe a differential graded Lie algebra controlling the deformation problem, and we prove an analog of a Mukai-Artamkin Theorem about the trace map.

final version accepted for publication in Canad. J. Math

Cited by in corpus (5)

• Formality conjecture for minimal surfaces of Kodaira dimension 0
• Deformations of Dolbeault cohomology classes
• Smoothing pairs over degenerate Calabi-Yau varieties
• Logarithmic $\partial \bar{\partial }$-lemma and several geometric applications (with an Appendix joint with Sheng Rao)
• Homotopy abelianity of the DG-Lie algebra controlling deformations of pairs (variety with trivial canonical bundle, line bundle)