I am a physics major who's studying mathematics, and I am interested in Topology and Geometry. I am mainly interested in Michael Atiyah's work in Algebraic Geometry and Chern-Simons Theories in physics.
What are the prerequisites in Abstract Algebra and Topology for Algebraic Geometry? I have already taken Real Analysis at Rudin Level, Group, Ring, and Module Theory at Dummit and Foote level. Are Field and Galois theories required to study Algebraic Geometry? Also, would Multivariate Analysis be helpful?