Math 483-1, Algebraic Geometry

Instructor: Mihnea Popa

Mihnea Popa
Office: Lunt 210
Tel: 847-491-5576
  • Meeting times: MWF 2-2:50, Lunt 102; FIRST MEETING WED JAN 17!
  • Office hours: M 3-4pm and by appointment
  • Textbook: 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"; 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 geometry, with a view towards 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 aim for the Kodaira embedding and vanishing theorem, and the weak and hard Lefschetz theorems. We will continue this material next quarter, when I will also discuss Hodge structures, polarizations, and complex Abelian varieties among other things.
Prerequisites: Solid knowlegde of algebra, decent knowledge of complex analysis, and a bit of manifolds and algebraic topology. (It would be especially useful to review differential forms before the class.)
Evaluation: Will be based on homework sets posted here roughly once every two weeks.