Allgemeine Informationen
| Veranstaltungsname | Vorlesung + Übung: Algebraic Geometry I |
| Veranstaltungsnummer | MTH-1480 |
| Semester | WS 2018/19 |
| Aktuelle Anzahl der Teilnehmenden | 8 |
| Heimat-Einrichtung | Algebra und Zahlentheorie |
| beteiligte Einrichtungen | Institut für Mathematik |
| Veranstaltungstyp | Vorlesung + Übung in der Kategorie Lehre |
| Voraussetzungen |
There are no particular pre-requisites apart bachelor-level knowledge of general topology, abstract algebra (familiarity with rings, fields, etc.) and linear algebra. Some previous notions of commutative algebra may be helpful, but everything needed will be recalled during the lectures. Although not strictly necessary, a good pre-reading for the course is Miles Reid's little blue book Undergraduate Algebraic Geometry (London Mathematical Society Student Texts) |
| Lernorganisation |
The lectures are based on my own notes, which will be made available on digicampus along the semester. Throughout the text there are a number of "Exercises" which are meant for self-testing one own's comprehension of the material. These exercises are not mandatory, but one who is willing to understand the material should do at least half of them. If you spot typos/mistakes in the notes please tell me! Coming to class: just come to the lectures if you think they are useful for you!!! If you don't come and prefer working on your own that it perfectly OK for me (you still have to submit your Homework though). Homework: on the last page of each lecture (in the notes) there are 2 exercises labeled "Homework". After the lecture takes place, the Homework exercises are due by the following Thursday at 12:12 Uhr. There are usually 2 lectures per week, whence 4 exercises per week. Homework must only be sent to me via email in pdf format (preferably LaTeX, but a handwritten scan is OK as far as it's readable). The email Subject should be in the format: "algebraic geometry I - Homework x" with x=1,2,3, etc. The email body can be left empty (but make sure your name appears somewhere!). Homework can (and should) be done in small groups, but each student must submit his own version. How to do the Homework: you do not have to prove every single statement you make. You don't have to be too formal. Use more words than symbols. Describing/sketching the idea behind the argument is the best way to do it. If you can not solve an exercise it is OK to just write down your attempts/thoughts about it. Problem sheets: a few problem sheets (probably 3) will be given throughout the semester. These are NOT meant to be sent to me, but rather should be just done in private (or in group). They are meant to be food for the mind. The oral exam will typically start with the discussion of one of these problems. Oral exam: after the end of the semester each student who has submitted at least 3/4 of the total amount of Homework exercises can request an oral exam. This can be done whenever you want throughout the next year. Write me an email at least 10 days in advance and we will fix an appointment. What will we discuss about during the oral exam: we will go through the material in the notes, mostly definitions, examples and theorems as well as possibly discussing some problems from the "Problem sheets". |
| Leistungsnachweis | The final score counts as follows: Homework 30%. Oral exam 70%. |
| Online/Digitale Veranstaltung | Veranstaltung wird online/digital abgehalten. |
| Hauptunterrichtssprache | englisch |
| Literaturhinweise |
I will be following the following (!): Texts: - R. Hartshorne "Algebraic Geometry" - J. Harris "Algebraic geometry, a first course" Notes: - R. Vakil "The rising sea: foundations of algebraic geometry" - A. Gathmann "Algebraic geometry" 2003/2004 I am omitting bibliographic details above because it's 2018 and web-search works. If you can't find one of these texts just tell me. |
| ECTS-Punkte | 9 |
