Kurs: Reading course: Classical examples in algebraic geometry - Details

Allgemeine Informationen

Veranstaltungsname	Kurs: Reading course: Classical examples in algebraic geometry
Semester	SS 2018
Aktuelle Anzahl der Teilnehmenden	2
Heimat-Einrichtung	Algebra und Zahlentheorie
Veranstaltungstyp	Kurs in der Kategorie Lehre
Erster Termin	Dienstag, 10.04.2018 14:00 - 15:30
Voraussetzungen	Linear algebra, basic abstract algebra (rings, groups), general topology.
Lernorganisation	In the first lecture I will give a brief introduction and present the topics of the first few seminars. In each following lecture a student will present the seminar and in the remaining time there will be informal discussion about the topic and/or the exercises. There will be weekly exercise sheets (1 exercise). Each student is expected to present at least 1 seminar in order to get 3 ECTS points. It is also possible to have 3 extra ECTS points, by preparing a second seminar.
Leistungsnachweis	The final grade will take into account the seminar(s), the exercises and the individual participation in class.
Veranstaltung findet online statt / hat Remote-Bestandteile	Ja
Hauptunterrichtssprache	englisch
Literaturhinweise	We will follow the book "Algebraic geometry, a first course" by Joe Harris
ECTS-Punkte	3+3 (MTH-3500 and MTH-3520)

Lehrende

• Marco Ramponi

Räume und Zeiten

Keine Raumangabe

Dienstag: 14:00 - 15:30, wöchentlich

Studienbereiche

• Mathematisch-Naturwissenschaftlich-Technische Fakultät > Institut für Mathematik > Master Mathematik

Kommentar/Beschreibung

Algebraic geometry is the study of the solution sets of systems of polynomial equations, by using algebraic methods to deduce geometric properties of the solution sets. The aim of this course is to uncover a number of topics in algebraic geometry, with as a guiding principle the idea of learning through the examples. Each seminar will have as a central theme one of the numerous classical examples or constructions of this beautiful mathematical discipline. The emphasis will be on intuition rather than formal rigour, the goal being to get acquainted with the examples and develop our geometrical reasoning.
This course will also serve as a useful introduction for students willing to follow the general course in algebraic geometry which will take place in the next academic year 2018-2019, where the modern formal machinery and the more abstract technology of the theory will be developed in detail.

Topics will include: affine and projective spaces, rational normal curves, Veronese embeddings, quadric hypersurfaces, Grassmannians, determinantal varieties and more.