Connections and L_∞ liftings of semiregularity maps

2021/02/09 by Emma Lepri, Lepri, Emma, Marco Manetti +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2102.05016

openalex publication_date 2021/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E^* be a finite complex of locally free sheaves on a complex manifold X. We prove that to every connection of type (1,0) on E^* it is canonically associated an L_∞ morphism g\colon A^{0, *}_X(Hom^*_OX(E^*,E^*))→ \dfracA^*,*_XA^{≥ 2,*}_X[2] that lifts the 1-component of Buchweitz-Flenner semiregularity map. An application to deformations of coherent sheaves on projective manifolds is given.

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