Hi, I posted this under General Physics but I thought I should post this under the math section too in case there are mathematicians who do not read posts under General Physics.(adsbygoogle = window.adsbygoogle || []).push({});

I read some papers online about Calabi-Yau surfaces but I have some basic questions about them if you can answer them for me.

1. Who proved that Calabi-Yau mfds fit into string theory? Why does C-Y surface fit into string theory, instead of any other surfaces?

2. I googled C-Y surfaces and saw many beautiful pictures of them. But why do they look like that? Do you have explanation other than the fact that they have a trivial canonical bundle?

3. What are different kinds of singularity types that can occur on a C-Y surface (just an intuition of them will be fine)? Why is the orbifold singularity considered to be the simplest singularity on a C-Y surface?

4. Why do singularities form on C-Y surfaces and what physical meaning do they have?

5. Why should we resolute singularities?

6. An orbifold is locally C^n/G where G is a finite subgroup of SL(n,C) and C = complex numbers. So where are the singularities? How do you see that?

7. What is a physics meaning (the physical perspective) of a canonical bundle?

8. How much of algebraic geometry do mathematicians and physicists use to study Calabi-Yau manifolds and string theory? I'm sure they do use PDE/ODE and differential geometry, correct?

Thank you in advance for your time!

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# Calabi-Yau surfaces and algebraic geometry for mathematicans

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