Math 296, D-modules in birational geometry

Instructor: Mihnea Popa

Mihnea Popa
Office: SC 537
Tel: 617-495-4825
email: mpopa@math.harvard.edu
  • Meeting times: MW 10:30-11:45 via Zoom
  • First meeting: Monday, January 25, 2021
  • Office hours: Tuesday 1.30-2.30pm, and by appointment
  • Recommended preliminaries and reading: Familiarity with fundamental algebraic geometry, roughly at the level of Hartshorne's book. Some basic familiarity with D-modules, as in Chapters 1-3 in the book by Hotta-Takeuchi-Tanisaki "D-modules, perverse sheaves, and representation theory", would be very helpful. I have posted notes that I wrote for a quite different version of this course as a link on my webpage. What I will need from those are some basic facts about the Bernstein-Sato polynomial and about the V-filtration on D-modules, found in Chapters 1 and 2. (I will review those, however briefly and without proofs.) I will indicate further sources as we go along, and will likely post lecture notes.
Brief course description: V-filtration and Hodge filtration on D-modules, and connections with singularities in birational geometry; vanishing and positivity theorems for Hodge modules; Hodge ideals; applications to singularities, holomorphic forms, generic vanishing, families of varieties, etc.
Technical details: The course will consist of Zoom delivered regular lectures. Zoom and other technical details and requirements will appear on the Canvas course page. Both pages will be updated regularly.