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| Two Applications of the ∂∂-Hodge Theory |
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Citation： |
Dingchang WEI,Shengmao ZHU.Two Applications of the ∂∂-Hodge Theory[J].Chinese Annals of Mathematics B,2024,45(1):137~150 |
| Page view： 322
Net amount： 401 |
Authors： |
Dingchang WEI; Shengmao ZHU |
Foundation： |
This work was supported by the National Natural Science Foundation of China (No. 12061014). |
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| Abstract： |
Using Hodge theory and Banach fixed point theorem, Liu and Zhu developed
a global method to deal with various problems in deformation theory. In this note, the
authors generalize Liu-Zhu’s method to treat two deformation problems for non-K¨ahler
manifolds. They apply the ??-Hodge theory to construct a deformation formula for (p, q)-
forms of compact complex manifold under deformations, which can be used to study the
Hodge number of complex manifold under deformations. In the second part of this note, by
using the ??-Hodge theory, they provide a simple proof of the unobstructed deformation
theorem for the non-K¨ahler Calabi-Yau ??-manifolds. |
Keywords： |
Complex structures, Deformations, (p, q)-Forms, Non-K¨ahler CalabiYau manifolds |
Classification： |
53C15, 53C56 |
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