TL;DR
This paper reviews recent advances in almost complex Hodge theory, focusing on the properties of Hodge numbers and their invariance under various geometric conditions in four-dimensional manifolds.
Contribution
It provides a comprehensive overview of the current state of almost complex Hodge theory, including criteria for invariance of Hodge numbers.
Findings
Hodge numbers can be almost complex, almost Kähler, or birational invariants in dimension four
Conditions determining the invariance of Hodge numbers are analyzed
Recent developments in the field are summarized
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 K\"ahler, or birational invariants in dimension four.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology