Course info

Meeting time: Tuesdays and Thursdays, 9-10:15 in SC120.

Office hours: Wednesdays 11-12 in SC242a, or by appointment.

Canvas link: here

Notes

Notes are regularly updated on GitHub.

• Local pdf (might be out of date at any given time, go to the GitHub for the most recent version)
• Here is how to submit a pull request

If you’re taking this class for credit, you will be responsible for contributing an appendix to the notes. Here is a potential list of appendices (I’ll update this more throughout the semester).

Content

This course will look at algebraic manifolds from an algebraic topology perspective. It will be loosely based on Hirzebruch’s 1956 text Topological methods in algebraic geometry, although we won’t assume any background knowledge of algebraic geometry as a prerequisite. Topics we will cover include:

• sheaves on algebraic manifolds, Cech cohomology
• the de Rham theorem
• fiber bundles and topological vector bundles
• characteristic classes (Chern, Pontryagin)
• oriented cobordism and the L-genus
• the index theorem
• complex cobordism and the Todd genus
• some basic Hodge theory
• Riemann-Roch for algebraic manifolds