## MAT 545: Complex Geometry
## Stony Brook Fall 2008 |
---|

The last office hours for the semester are Monday, 12/15, 5-7 in 3-111 and Tuesday, 12/16, 9-10 in P-143. While this is after the class is over and the last problem set is due, you are very much encouraged to stop by with any questions you might have.

**Handouts**

- general information about the course
- Notes on Connections. The proof of Lemma 2.2 on pp7,8 is a solution to the first part of (2) of Problem 3 on PS3 and implies the second part as well. Lemma 2.3 is related to some of the attempted solutions.
- Notes on Lefschetz Decomposition
- Solutions to Problem Set 5
- Solutions to Problem Set 7

*Name:*
Aleksey Zinger
*E-mail:* azinger@math
*Phone:* 432-8618

*Office:* Math Tower 3-111
*Office Hours:* Tu 5-7 in 3-111, W 9-10 in P-143

Date |
Topic |
Read |
Problem Set |

9/2, Tu | Functions of one complex variable | pp1-5 | #1 |

9/4, Th | Functions of several complex variables | pp6-9 | |

9/9, Tu | Analytic varieties | pp9-14 | |

9/11, Th | Complex manifolds | pp14-20 | |

9/16, Tu | Dolbeault cohomology | pp23-27 | #2 |

9/18, Th | Analytic subvarities and integration | pp12-14,27-34 | |

9/23, Tu | Sheaves | pp34-38 | |

9/25, Th | Sheaf cohomology | pp38-49 | |

9/30, Tu | no class | ||

10/2, Th | Review/overview of algebraic topology | pp49-60 | #3 |

10/7, Tu | Intersections of cycles in manifolds | ||

10/9, Th | no class | ||

10/14, Tu | Intersections of analytic cycles | pp60-67 | |

10/16, Th | Hermitian vector bundles | pp67-80 | |

10/21, Tu | Hodge Theorem and applications | pp80-84,100-106 | #4 |

10/23, Th | Elliptic operators on compact manifolds | ||

10/28, Tu | Fourier series and applications | pp84-91 | |

10/30, Th | Proof of elliptic regularity | pp92-100 | |

11/4, Tu | |||

11/6, Th | Kahler manifolds and Hodge identities | pp106-115 | #5 |

11/11, Tu | Hodge and Lefschetz decompositions | pp116-126 | |

11/13, Th | Line bundles and divisors | pp128-136 | #6 |

11/18, Tu | Adjunction formulas, first chern class | pp136-148 | |

11/20, Th | Vanishing theorems | pp148-156,159-161 | |

11/25, Tu | Some applications | pp156-159,161-164 | |

11/27, Th | no class | ||

12/2, Tu | Maps to projective spaces | pp176-182 | #7 |

12/4, Th | Blowups | pp182-189 | |

12/9, Tu | Kodaira Embedding Theorem | pp189-192 | |

12/11, Th | no class | ||

12/15, Mo | Algebraic varieties | pp164-176 |

This page is maintained by Aleksey Zinger.