## MAT 615: Complex Curves and Surfaces
## Stony Brook Spring 2009 |
---|

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 |

This page is maintained by Aleksey Zinger.