## MAT 545: Complex Geometry
## Stony Brook Fall 2019 |
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- Notes on Cech cohomology from here. These contain solution to PS2 #6.
- More on pseudocycles.
- Notes on connections and more. The proof of Lemma 2.2 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 this also.
- Notes on Lefschetz Decomposition
- Solutions to Problem Set 5
- Solutions to Problem Set 7
- Wrapup of pf of Kodaira Embedding Theorem

Date |
Topic |
Read |
Problem Set |

8/27, Tu | Functions of one complex variable | pp1-5 | #1 |

8/29, Th | Functions of several complex variables | pp6-9 | |

9/3, Tu | Analytic varieties | pp9-14 | |

9/5, Th | Complex manifolds | pp14-20 | |

9/10, Tu | Dolbeault cohomology | pp23-27 | #2 |

9/12, Th | Analytic subvarities and integration | pp12-14,27-34 | |

9/17, Tu | Sheaves | pp34-38 | |

9/19, Th | Sheaf cohomology | pp38-49 | |

9/24, Tu | Review/overview of algebraic topology | pp49-60 | #3 |

9/26, Th | Intersections of cycles in manifolds | ||

10/1, Tu | Intersections of analytic cycles | pp60-67 | |

10/3, Th | Hermitian vector bundles | pp67-80 | |

10/8, Tu | Hodge Theorem and applications | pp80-84,100-106 | #4 |

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

10/17, Th | Fourier series and applications | pp84-91 | |

10/22, Tu | Proof of elliptic regularity | pp92-100 | |

10/24, Th | |||

10/31, Th | |||

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

11/7, Tu | Hodge and Lefschetz decompositions | pp116-126 | |

11/12, Tu | Line bundles and divisors | pp128-136 | #6 |

11/14, Th | Adjunction formulas, first chern class | pp136-148 | |

11/19, Tu | Vanishing theorems | pp148-156,159-161 | |

11/21, Th | Symplectic Topology Seminar in Math 5-127 | ||

11/26, Tu | Some applications | pp156-159,161-164 | #7 |

12/3, Tu | Maps to projective spaces | pp176-182 | |

12/5, Th | Blowups | pp182-189 |

This page is maintained by Aleksey Zinger.