Mihnea Popa Office: SC 537 Tel: 6174954825 email: mpopa@math.harvard.edu 

Brief course description: Some of the topics we will cover are: affine and projective varieties, Hilbert's Nullstellensatz, tangent spaces, smoothness, dimension theory, morphisms and rational maps, Grassmannians, correspondences, degree, Bezout's theorem, Hilbert polynomial, divisors and linear systems on curves, the RiemannRoch theorem. 
Prerequisites: Basic algebra (fields, rings, modules, polynomial rings) as in Math 123 or an equivalent class; also a modicum of commutative algebra (e.g. prime and maximal ideals, Noetherian rings) as in Ch.1 of AtiyahMacDonald is recommended reading. 
Requirements: Regular attendance is expected. There will be weekly homework, posted on Canvas and on this page every Wednesday, and due the following Wednesday. Homework is the most important component of this course, counting for 60% of your grade. Normally no late homework will be accepted, but the lowest score will be dropped. You are encouraged to collaborate on the homework problems, but you must write your own solutions and properly acknowledge any collaboration, or help you receive from others. There will also be a takehome final exam that will account for 40% of the final grade. 
Homework : 