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MAT 615: Complex Curves and Surfaces
Stony Brook Spring 2009 |
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PS6 has been updated; it now contains 10 exercises, including details for the important argument on pp561-563. Please let me know if there are any issues with the exercises.
Here is general information about the course (updated 01/26).
Name:
Aleksey Zinger
E-mail: azinger@math
Phone: 432-8288
Office: Math Tower 3-111
Office Hours: Tu 2:30-4 in 3-111, W 10-11:30 in P-143
In the Read column below, G&H a.b refers
to Chapter a, Section b in Griffthis and Harris.
| Date | Topic | Read | Problem Set |
| 01/27, Tu | Introduction | G&H 2.0,2.1 | #1 |
| 01/29, Th | Some key properties | ||
| 02/03, Tu | Jacobian of a curve | G&H 2.2 | |
| 02/05, Th | Proof of Abel's Theorem | ||
| 02/10, Tu | Jacobi Inversion | #2 | |
| 02/12, Th | Riemann-Roch for a curve | G&H 2.3 | |
| 02/17, Tu | Castelnuvo bound | ||
| 02/19, Th | Riemann count | ||
| 02/24, Tu | no class | ||
| 02/26, Th | |||
| 03/03, Tu | Curves of low genus/degree | ||
| 03/05, Th | Elliptic curves and moduli problem | Hain A,1,2 | #3 |
| 03/10, Tu | |||
| 03/12, Th | Orbifolds | Hain 3 | |
| 03/17, Tu | Modular forms | Hain 4 | |
| 03/19, Th | Relation with plane cubics | Hain 5 | #4 |
| 03/24, Tu | Moduli space of elliptic curves | ||
| 03/26, Th | Blowups and blowdowns of surfaces | G&H 4.0,4.1 | |
| 03/31, Tu | Curves on surfaces | pp396-397 pp498-510 | |
| 04/02, Th | |||
| 04/07, Tu | no class | ||
| 04/09, Th | |||
| 04/14, Tu | Rational maps on surfaces | pp489-498 pp510-512 |
#5 |
| 04/16, Th | Rational ruled surfaces | G&H 4.3 | |
| 04/21, Tu | Minimal rational surfaces | ||
| 04/23, Th | Detecting rational surfaces | G&H 4.4 | |
| 04/28, Tu | Irrational ruled surfaces | G&H 4.5 | #6 |
| 04/30, Th | |||
| 05/05, Tu | Other types of surfaces | ||
| 05/07, Th | Summary | ||