Dolbeault Type Cohomology Groups of Infinitesimal Deformations and Their Applications

2023/04/20 by Jiezhu Lin, Lin, Jiezhu, Xuanming Ye +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2304.10355

openalex publication_date 2023/04/20 · openalex created_date 2023/04/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish a kind of Dolbeault type cohomology groups for the purpose of studying the varying of complex structure invariants in infinitesimal deformations of any order. We give a concrete description of the higher order Kodaria-Spencer maps by using these cohomology groups. We reformulate the obstruction formulas within the framework of these cohomology groups and give a new proof for the formulas.

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