I'd like some introductory references for deformation theory in algebraic geometry. I'm interested in survey articles too but I primarily want references which give all the definitions and go through the basics carefully and also give some idea of the link between deformation theory and intersection theory and/or K-theory. Texts with examples would be particularly nice. Applications to representation theory would also be useful to me.
As a specific example, I would like to understand how deformation theory helps in understanding the geometry of the Hilbert scheme of points on a surface (and the geometry of more general moduli spaces like Nakajima quiver varieties, if possible).
My background in geometry is Hartshorne and some material on constructible sheaves and D-modules. I've also come across some deformation theory from the representation theory side.
Thank you for the help.
Edit: I'm also perfectly happy with references that only deal with complex algebraic geometry.
Best Answer
You could try Sernesi's book (deformations of algebraic schemes).