SYLLABUS MATH 531: Algebraic Geometry
Algebraic Geometry is the study of solution sets
of systems of polynomial
equations in several variables with complex coefficients
(or more generally with coefficients in an algebraically closed field).
The solution sets
are viewed as geometric/topological objects
and geometric/topological ideas play a central role in the subject.
Today Algebraic Geometry is one of the central
subjects of pure mathematics, at the confluence of number theory,
differential geometry, and theoretical physics.
The prerequisites are minimal: only a course in graduate
(or even undergraduate) abstract algebra is needed.
I will follow Shafarevich's book "Basic Algebraic Geometry,
Vol 1" and I will complement
it with some material from Serre's "Algebraic groups and class fields".
None of these books is required; they are merely recommended.
I will cover: affine and projective varieties, normalization, projections,
divisors, differentials, Weil's proof of Riemann-Roch for curves.
Grading will be based upon attendance
plus a set of homework problems to be assigned in class.
Qualified students with disabilities needing
appropriate academic adjustments
should contact me as soon as possible to ensure your needs
are met in a timely manner. Handouts are available
in alternative accessible formats upon request.
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