Deformations of cohesive modules on compact complex manifolds

2023/08/02 by Zhaoting Wei, Wei, Zhaoting
Mathematics · Physics and Astronomy · #18D20 #32G08 #32Q99 #53C05 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2308.01266

openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This generalizes the deformation theory of holomorphic vector bundles and coherent sheaves. We also develop the theory of Kuranishi maps and obstructions of deformations of cohesive modules and give some examples of unobstructed deformations.

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