Math 517-2, D-modules in birational geometry

Instructor: Mihnea Popa

Mihnea Popa
Office: Lunt 226
Tel: 847-491-5576
  • Meeting times: MWF 2-2:50, Lunt 102
  • Office hours: M 3-4pm and by appointment
  • References: For parts of the course related to the basic theory of D-modules I will continue to use the textbook "D-modules, perverse sheaves, and represenatation theory" by R. Hotta, K. Takeuchi and T. Tanisaki. I will also use R. Lazarsfeld's "Positivity in algebraic geometry" for topics in birational geometry, like multiplier ideals. A few papers by M. Kashiwara, B. Lichtin, M. Saito, etc, that I will mention in class, will be discussed as well.
  • Other useful references: Later on we will make use of M. Saito's "Modules de Hodge polarisables", and C. Sabbah and C. Schnell's "MHM project"
Brief course description: Here are some of the new topics that we will discuss this quarter: more on holonomic and regular D-modules; the rationality of the roots of Bernstein-Sato polynomial, and the more precise relationship between these roots and invariants in birational geometry; the analytic continuation of the archimedean zeta functions via Bernstein-Sato polynomials; the connection between multiplier ideals in complex geometry and the V-filtration; more on holonomic and regular D-modules; filtered D-modules and de Rham complexes; first steps towards understanding the Hodge filtration on mixed Hodge modules Notes will be posted occasionally.