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There are lots of references. Mainly every textbook which treats Hodge theory. Try to look at:

• Voisin: Hodge theory and complex algebraic geometry. I
• Huybrechts: Complex geometry
• Wells: Differential analysis on complex manifolds
• Griffiths, Harris: Principles of algebraic geometry

There, you will find mainly the proof in the case $n=2$, which is used to prove the Lefschez theorem on $(1,1)$-classes. The general case is a straightforward adaptation of that argument.

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There are lots of references. Mainly every textbook which treats Hodge theory. Try to look at:

• Voisin: Hodge theory and complex algebraic geometry. I
• Huybrechts: Complex geometry
• Wells: Differential analysis on complex manifolds
• Griffiths, Harris: Principles of algebraic geometry