Math 232A, Complex Algebraic Geometry

Instructor: Mihnea Popa

Mihnea Popa
Office: SC 537
Tel: 617-495-4825
  • Meeting times: MW 1.30-2.45 in SC 222; first meeting September 6
  • Office hours: Wednesday 3-4, and by appointment
  • CA: Wanchun (Rosie) Shen -
  • Recommended texts: There won't be a single textbook, but I will mostly use Griffiths-Harris "Principles of Algebraic Geometry", Huybrechts "Complex Geometry: An Introduction" and Voisin "Hodge Theory and Complex Algebraic Geometry I"
  • Other useful references: Mumford "Complex Projective Varieties"; Hartshorne "Algebraic Geometry"; Gunning-Rossi "Analytic functions of several complex variables"; Wells "Differential analysis on complex manifolds"
Brief course description: I will give an introduction to the complex analytic side of algebraic geometry, (very) roughly modeled after the first two-three chapters in Griffiths-Harris. We will discuss the de Rham theorem, the decomposition of forms according to type, the Kaehler condition, cohomology of analytic sheaves, and how all of this leads to Hodge theory. We will then aim for the Kodaira embedding and vanishing theorem, and the weak and hard Lefschetz theorems, plus some explicit geometry through examples. We will continue this material next semester, when I will also discuss Hodge structures, polarizations, complex Abelian varieties and deformations of complex structures, among other things.
Prerequisites: Solid knowledge of algebra, decent knowledge of complex analysis, and a bit of manifolds and algebraic topology. (It would be particularly useful to review differential forms before the start of the course.) Especially since this is not the more common algebraic introduction to the subject, it will be helpful to have previously seen some basic algebraic geometry at the level of Math 137.
Evaluation: Will be based on regular homework sets.