Math 514-2, Topics in Geometry

Mihnea Popa
Office: Lunt 210
Tel: 847-491-5576
  • Meeting times: MWF 12-12:50, Lunt 101
  • First meeting: Wednesday, January 4, 2017
  • Office hours: F 1-2 and by appointment
Recommended texts. For the first part I will use "Positivity in Algebraic Geometry" by R. Lazarsfeld quite a bit. Other recommended texts are J. Kollár and S. Mori "Birational Geometry of Algebraic Varieties" and C. Voisin Hodge Theory I, II. The paper "Hodge ideals" by M. Mustata and myself will be useful for the last part. For a quick introduction to intersection numbers, positivity, vanishing theorems, etc., you can consult my lecture notes from a previous course:
Brief course description: The goal of the course is introduce various ideal sheaves associated to singularities in birational geometry, like adjoint, multiplier, and Hodge ideals, and to explain how they are used in applications. As an example, one such application will be the Angehrn-Siu bound on effective freeness for adjoint bundles. This background material consists of basic facts from higher dimensional geometry and Hodge theory; later on there I will use (and cover) a bit of D-module theory as well.
This is not required, but I encourage you to turn in solutions to the various exercises I will include in the lectures. There will be small projects towards the end of the class.