I have been doing some reading on algebraic geometry, in particular singularity resolutions. All the examples I am familiar with in physics correspond to singularities of the extra dimensions (e.g. blow up of orbifold singularities).
As algebraic geometry appears in supersymmetric QFTs without mentioning string theory through the moduli space of vacua, I was wondering if there are any simple examples where the moduli space of a given theory with a singularity that can be resolved by blow up.
I'm looking for an example without the need to introduce the whole machinery of string theory, where the exceptional divisor has a simple(ish) physical interpretation.