Math 271: Kodaira dimension and families of varieties

Instructor: Mihnea Popa

Mihnea Popa
Office: SC 537
Tel: 617-495-4825
email: mpopa@math.harvard.edu
  • Meeting times: MW 10:30-11:45
  • First meeting: Wednesday, August 31, 2022
  • Office hours: Monday 11.45-12.45pm, or by appointment
  • Recommended preliminaries and reading: Familiarity with fundamental algebraic geometry, roughly at the level of Hartshorne's book plus the first two chapters in Griffiths-Harris. Some basic familiarity with various notions of positivity for line bundles, as in Ch. 1 and 2 in Lazarsfeld's book. The second part of the course will use some Hodge theory, as in the first volume of Voisin's book, and eventually a bit of D-module theory as in the book by Hotta-Takeuchi-Tanisaki plus Hodge module theory as in the Math 296 notes on my webpage. I will briefly review some of these notions and indicate more precise sources as we go along.
Brief course description: Iitaka dimension of line bundles and Kodaira dimension; birational classification of algebraic varieties; Iitaka's subadditivity conjecture; positivity for line bundles and vanishing theorems; weak positivity for coherent sheaves; variation and Viehweg's conjecture; algebraic hyperbolicity of parameter spaces; superadditivity of Kodaira dimension for smooth morphisms
Lecture notes