I'm trying to learn about D-modules for computing intersection cohomology but I'm having trouble coming up with explicit constructions of D-modules on projective varieties. Since this is an involved process, I'll split this up into multiple questions:

1. How do I construct D-modules over complex projective space
2. How do I construct D-modules over smooth projective varieties
3. How can I use the constructions from (1) to find D-modules with
   geometric support on singular varieties?

My goal is to start looking at D-modules on Fermat curves $$ \text{Proj}\left( \frac{\mathbb{C}[x,y,z]}{x^n + y^n - z^n} \right) $$ and answer the question I raised here