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 ⊂ schemes ⊂ stacks. However I am looking for specific (underived) scheme constructions like Fano schemes, Hilbert schemes, scheme-theoretic interesections etc



Applications of schemes to mathematical physics
In string theory, gauge symmetries on D-branes can be studied using classical scheme theory.


This was introduced around the late 1990s and early 2000s, cf. [this 1998 paper](https://arxiv.org/abs/hep-th/9811197), [this 2000 note](https://arxiv.org/abs/hep-th/0008150), [these 2003 notes](https://arxiv.org/abs/hep-th/0307245), and [this 2007 paper](https://arxiv.org/abs/0709.1515) to start.


