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I don't think this is a bad question. I think it should be re-opened. In the comments I have given the answer that I would give to this question if it were not closed.
And I've reopened.
I propose to copy and paste the comment thread over to here, delete it and replace it with a link to this thread.
The comment thread at this moment:
This question has been closed. It is way too broad for MO, which is for specific, focused questions. – Pete L. Clark 8 hours ago
This is not a bad question! Aaron Bergman's answer to this question mathoverflow.net/questions/30629/… for example might be a good answer to OP's question. – Kevin Lin 7 hours ago
Essentially: algebraic geometry sometimes enters the picture in string theory and physics because, while we start with a compact Kähler manifold, for some reason or another we maybe get an integral Kähler class, and thus our manifold is projective by the Kodaira embedding theorem, and thus it is algebraic by Chow's theorem. Conversely, we may be actually interested in possibly non-algebraic compact Kähler manifolds in the physics or string theory, but the algebraic manifolds will provide at least a pretty big class of nice examples to play with. – Kevin Lin 7 hours ago
And at least for smooth projective algebraic varieties, GAGA theorems tell us that many things (like e.g. sheaf cohomology) are the same whether we consider our space as an algebraic variety or as an analytic thing. – Kevin Lin 7 hours ago
I agree with Kevin Lin that the question (if phrased more clearly) is actually interesting. – Spiro Karigiannis 4 hours ago
I think the question should not have been closed. – Kevin Walker 2 hours ago
Further meta discussion should go in the meta thread Kevin Lin created: meta.mathoverflow.net/discussion/826/… – Ryan Budney 1 hour ago
I have deleted my comments and added an answer. Thanks for re-opening this question!