Almost complex Hodge theory

2022/03/17 by Zhang, Weiyi
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.09274

Abstract

We review the recent development of Hodge theory for almost complex manifolds. This includes the determination of whether the Hodge numbers defined by ∂-Laplacian are almost complex, almost Kähler, or birational invariants in dimension four.

Related

• From Smooth to Almost Complex
• Hodge theoretic results for nearly Kähler manifolds in all dimensions
• Almost Kähler Kodaira-Spencer problem
• Kodaira dimensions of almost complex manifolds I
• Hodge decomposition and Hard Lefschetz Condition on almost Kähler manifolds