Constructible sheaves and vanishing cycles
Time and place
Room 509, Cosmology Bldg., NTU Campus
Tuesdays 16:30 – 18:20, Wednesdays 10:20 – 12:10
Starting the week of October 13th, ending the week of January 6th.
Description
We will introduce the formalism of constructible sheaves on complex algebraic varieties, which is the basis for the cohomological study of the geometry and topology of algebraic varieties. In the first part, we will cover derived categories of sheaves, the six functors, constructibility, and Verdier duality. In the second part, we will study nearby and vanishing cycles sheaves, which are used to analyze the topology of degenerating families.
Lecture notes
Exercises
There will be one exercise sheet per week, usually uploaded on Thursday morning. It should be submitted by Friday of the following week, by email or in my mailbox (Astro-Math Bldg., 6F). A minimum average of 20 points per sheet is required.
Sheet 1
Sheet 2
Sheet 3 (2025-11-05: Ex. 4 was corrected)
Announcements
- The Tuesday lecture has been pushed by 10 minutes (starting at 16:30 instead of 16:20).
- There will be no lectures during the week of November 3–7. To make up for this, there will be an additional two lectures in the first week of January.
- The lectures are being recorded on video. Contact me for the link.