Cubic Hypersurfaces · Math 732
The goal of this course is an in-depth study of the geometry of cubic hypersurfaces. We will study many aspects of algebraic geometry through the lens of cubic hypersurfaces: rationality problems, Hodge theory and Torelli theorems, Fano varieties of lines and hyperK manifolds, and derived categories. The course will be example driven and will start with some general theory of cubic hypersurfaces, a study of their Fano varieties, and their moduli spaces. In the latter portion of the course we will carry out an in-depth study of cubics in dimensions 2, 3, and 4.
location · East Hall 1866
class time · Tues/Thurs 1PM-2:30PM
instructor · David Stapleton (he/him)
call me · David or Professor Stapleton
email · dajost@umich.edu
office · East Hall 4839
office hours · Tues 9:00AM-11:30AM
prerequisites
MATH 631-632 or equivalent.
recommended textbooks
The Geometry of Cubic Hypersurfaces by Daniel Huybrechts.
participation
If you have not yet passed your prelim exam, or do not plan to pass it by the end of the semester. I would like you to submit solutions to 4 of the exercises every 4 weeks. If you have questions about any exercise, please come talk to me! You are encouraged to work together on these problems (and to talk to older students as well!), but you should submit your own work to me.
