**Sommersemester 2012**

**Commutative Algebra and Algebraic Geometry**

**(Kommutative Algebra und Algebraische Geometrie)**

**(326.212 lecture & 326.214 exercises)**

**Prof. Franz Winkler**

**Time/Room:**

Lecture: |
Tue | 14:30 - 16:15 | in | HS 11 | |

Fri | 10:15 - 11:45 | in | HS 14 | ||

Exercises: |
Tue | 16:15 - 17:00 | in | HS 13 | |

First Lecture: | Fri | 09.03.2012 | |||

No lecture on May 18 | |||||

and on May 22 |

Classical algebraic geometry is the theory of algebraic curves, surfaces, and varieties in higher dimensions. Nowadays, such algebraic varieties are of high importance in computer aided geometric design, computer vision, cryptography, and other application areas.

The algebraic theory which allows us to compute with such varieties is called commutative algebra. It is concerned with polynomial equations, polynomial ideals, and polynomial and rational mappings.

Participants in the course are expected to be acquainted with basics in (computer) algebra. Much of the material for this course will be taken from the book

J.R. Sendra, F. Winkler, S. Perez-Diaz, | ||

Rational Algebraic Curves - A Computer Algebra Approach, |
||

Springer-Verlag (2008) |

Lecture Notes: |
00-title.pdf |

01-intro.pdf | |

02-elimination.pdf | |

03-algset.pdf | |

04-corr.pdf | |

05-proj.pdf | |

06-func.pdf | |

07-local.pdf | |

08-para.pdf | |

09-puiseux.pdf | |

10-dimension.pdf | |

references.pdf |