Joint deformations of manifolds, coherent sheaves and sections

2025/07/27 by Iacono, Donatella, Manetti, Marco
#13D10 #14B10 #14D15 #17B70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.20276

Abstract

We describe a differential graded Lie algebra controlling infinitesimal deformations of triples (X,F,σ), where F is a coherent sheaf on a smooth variety X over an algebraically closed field of characteristic 0 and σ∈ H⁰(X,F). Then, we apply this result to investigate deformations of pairs (variety, divisor).

Citations

• On the local structure of the Brill-Noether locus of locally free sheaves on a smooth variety
• On the geometry of anticanonical pairs
• Unobstructedness of deformations of Calabi-Yau varieties with a line bundle
• Hodge theoretic aspects of mirror symmetry
• Notes on Grothendieck topologies, fibered categories and descent theory
• Descent of Deligne groupoids

Related

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• Non-commutative deformations of perverse coherent sheaves and rational curves