# Algebraic geometry reference

I believe similar reference requests have been asked previously but I think mine is somewhat specific. I am interested in learning algebraic geometry.

My experience so far has been with complex projective varieties and schemes of finite type over $$\mathbb{C}$$, with divisors, sheaves, vector bundles, and cohomology on Riemann surfaces, and analytic sheaves. I am comfortable with commutative algebra at the level of Atiyah-MacDonald and Kleiman's texts. My interest leans towards complex geometry, but I would enjoy getting a good understanding of the algebraic/functorial picture too.

I tried reading Hartshorne but I found the style to be dry and not insightful. I do plan to work through it eventually, but would want a reference that covers similar amounts of theory and feels intuitive given my background.

My current picks are Cutkosky's book, "Introduction to algebraic geometry"; for schemes, I am reading Ulrich and Wedhorn's text, and for cohomology, my pick is Serre's FAC.

I'm wondering if these will cover roughly the same material as the first three chapters of Hartshorne; what I would be missing out on, would there be overlap bits that I can gloss over, and what else will be an intuitive reference for learning the subject?