The Jumping Phenomenon of Hodge Numbers

2007/04/16 by Xuanming Ye, Ye, Xuanming · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #math.AG #math.DG

paper · pdf · doi:10.48550/arxiv.0704.1977

arxiv created 2007/04/16 · openalex publication_date 2007/04/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a compact complex manifold, consider a small deformation ϕ: X → B of X, the dimension of the Dolbeault cohomology groups H^q(X_t,Ω_Xt^p) may vary under this defromation. This paper will study such phenomenons by studying the obstructions to deform a class in H^q(X,Ω_X^p) with the parameter t and get the formula for the obstructions.

Cited by

• The jumping phenomenon of the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups

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