Math 137, Algebraic Geometry

Instructor: Mihnea Popa

Mihnea Popa
Office: SC 537
Tel: 617-495-4825
  • Meeting times: MW 10:30-11:45 in SC 309
  • First meeting: Monday, January 23, 2023
  • Office hours: Wednesday 12-1pm, and by appointment
  • CAs:     Eliot Hodges     and     Hahn Lheem
  • Recommended texts: I will not use a particular textbooks, but will appeal to a number of standard sources, like R. Hartshorne's "Algebraic Geometry", I. Shafarevich's "Basic Algebraic Geometry I", J. Harris' "Algebraic Geometry" or W. Fulton's "Algebraic Curves". Occasionally it may be helpful to consult commutative algebra texts, like M. Atiyah and I. G. MacDonald's "Introduction to Commutative Algebra", or D. Eisenbud's "Commutative Algebra with a view toward Algebraic Geometry".
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 Riemann-Roch 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 Atiyah-MacDonald 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 take-home final exam that will account for 40% of the final grade.
Homework :