Books about Kähler manifolds, Ricci flatness and other things

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Summary:: Books about Kähler manifolds, Ricci flatness and similar things

Hi,

I have an MSc degree in electronics, and I worked with IT. I was always interested in theoretical physics and did extra studies of this in my youth. Now as a pensioner I do private studies for fun. I have studied quantum physics, elementary particle physics, general theory of relativity, and group theory, and now I am into string theory. I run into some mathematics that is new to me, like Kähler manifolds, Ricci flatness, Chern classes, canonical bundles, metrics with global holonomy, and similar things. I look at them in Wikipedia, but I feel the need for a more wholesome treatment, that is books about these things. So please give me tips about good books! I will be grateful.
 
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Thank you very much! That book looks really good. I will get it and start reading it, hoping to understand it. Now you have made me smile and feel good. Thank you again! :) I attach a sunrise picture with the moon, seen from a window in my home.
 
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