Could anyone cite some applications or developments in mathematical physics or string theory that use schemes?
I find curious the fact that while things like derived algebraic geometry and stacks have certain applications to mathematical physics I cannot find such applications for the case of (underived) schemes.
Just to clarify: I know that for example you can have Calabi-Yau threefolds that are projective algebraic varieties and that in some sense algebraic varieties $\subset $ schemes $\subset $ stacks. However I am looking for specific (underived) scheme constructions like Fano schemes, Hilbert schemes, scheme-theoretic interesections etc