Enumerative Geometry Math 7800-1
Instructor: Y.P. Lee, JWB 305
Office Hours:
Any time my office door is open.
Lecture
Time and Room MWF 12:55-13:45 at LCB 225 and Thursdays 10:45-11:35 at JWB 333
Course Information
Website: http://www.math.utah.edu/~yplee/teaching/7800f23/
Textbook: None, but will provide references and sometimes typed notes.
Course Description.
The main theme of this class is a survey of enumerative geometry, including Gromov--Wittne theory, Donaldson--Thomas theory and their (categorical) variants.
My plan is to start with very quick introduction to the theory of moduli and algebraic stacks, then move on to define virtual fundamental classes in GW, DT and other theories.
Ultimately, the foundations of this subject have moved towards the derived algebraic geometry. We might not be able to cover it in this semester, but it opens a rich field for research and is worth investigating.
Reading list:
- 13/2 ways of counting curves, this is a survey paper aimed at general algebraic geometers.
- For treatments on moduli and Hilbert schemes, see
- Arbarello, Cornalba, Griffiths, (Harris), Geometry of algebraic curves II (Chapter 1).
- E. Viehweg, Quasi-projective moduli for polarized manifolds (Chapter 1).
- For introduction to stacks, there are many (more recent) papers and sites freely available on the internet. Older sources include P. Deligne and D. Mumford's Publ. IHES article The Irreducibility of the Space of Curves of Given Genus as well as Section 1.4 of the book Degeneration of Abelian Varieties by Ching-Li Chai and Gerd Faltings.
- Intrinsic normal cones, a foundational paper on virtual fundamental classes.
- Kontsevich--Soibelman.
- More later.
Grading Policy: In accordance with the departmental tradition, A is
given to all participating students.
Department Schedule •
Y.P.'s teaching page
•
Y.P.'s homepage
