This course will not be diving straight into Hartshorne as students hold on for dear life. Rather, we will go deliberately through the first steps in understanding varieties in projective space (so our first definition will not be "A scheme is ..."). We will tackle some more of the classical topics like elliptic curves, hypersurfaces, Grassmannians, etc. with a more complete syllabus to be compiled based on students' need and research interests.
Shafarevich, Basic Algebraic Geometry I (Varieties in Projective Space)
A definite prerequisite is Math 551 or equivalent. Math 552 is useful as a pre- or co-requisite.